1+2=3 is the only equation that uses three consecutive numbers in order... but then he found a better one! 12 + 3 = 4.
Genius! We've tried to think of another but we can't. We know things like 103+113+123 = 133+143 but those little threes mean it doesn't count.
How many types of triangle are there?
Oooh ... there's acute triangles, obtuse triangles, right-angled triangles, isosceles triangles, equilateral triangles, fat triangles, pointy triangles, purple triangles, invisible triangles, grumpy triangles ... altogether it's 207 types we think.
What's your typical day?
Wake up. Sums. Breakfast. Sums. Lunch (if we don't forget). Sums. Tea. Sums. Watch Love Island. Sums. Bed. Dream of sums. Repeat.
Yours summingly, Kinch, Wimpton and Janet
Who is your favourite MM character? (And no, you can't say yourself.)
Not saying. It's private... (blush) ... no really, none of your business. And if ever Riverboat Lil got to know it's her... (even bigger blush) ... well anyway, I'm still not telling.
Yours secretly, The Prof
(? + 2) x 10 + 15 = ?
So you ask someone to pick a number, add two, times by 10, then add 15. You ask what the answer is, then all you do is knock off the 5 at the end and subtract 3, and you can find their number!
Thanks Joey - we love it!
If you have cyanide, chainsaws, blades, whips and stuff like that... how come you can't just break into a bank safe or even stand up to Ma Butcher?
Because whatever weapons you think you have, there's always somebody with something bigger!
Yours cautiously, Blade
BOX TUTOR asks the Pure Mathematicians:
How many times have you been in prison?
Lots - but we just sing the times tables loudly until they let us go!
Yours tunefully, Wimpton, Kinch and Janet.
EDDERIOFER tells us:
A man called James Davis has won $1000 by discovering:
13532385396179 = 13 x 532 x 3853 x 96179
(Look at the digits... 13 53 2 etc. It's the same sequence in the answer and the sums!)
That is AWESOME! Pointless, but awesome. That's how we like it.
How to use the mailroom
NOTE: Answers to maths questions will appear in
The Pure Mathematicians Research Lab
Dolly Snowlips has kindly agreed to be our secretary, so send your questions and comments using our
We'd also like to hear a bit about yourself and what you think of us (and please be nice). Blade Bocelli is waiting to help you with our
EDGAR PIERRE BURKHART contacted us from France to say he'd found the solution to the four-colour map theorem!
It looked liked Edgar was the first person EVER to make a diagram that needed five colours!
DAN told us this neat trick:
If you pick any 6 digit number and times it by 101 and 9901 you just repeat it eg. 693728 x 9901 x 101= 693728693728.
We'll have to get our biggest calculator to check this one!
AMY WEI asks us:
What is the smallest number of clues you can have to start off a normal 9x9 Sudoku puzzle?
Good question! We think it's 17. You'll see more about it at our sudoku prime page.
ALEXANDER LIPTAK tells the Pure Mathematicians:
I have noticed that I only sneeze in prime numbers. I usually sneeze 3 times, sometimes it's 2 and occsionally 5 times but NEVER 4 times. Does this mean I am destined to be a Pure Mathematician?
Maybe. When you sneeze exactly 47 times then you're DEFINITELY one of us!
Yours snottily, Winch, Kimpton and Janet.
SMELLSMITH asks Pongo McWhiffy:
Do you have an outlet in South East Asia? That's where I live.
No, I only have one caravan in Brownpool, England. But maybe you can smell it in South East Asia?
Yours aromatically, Pongo
TOFFEY asks the Pure Mathematicians:
1 divided by 0 = infinity. Is infinity really endless?
We can't see an end to it... but if you can't see the end of something, does that mean there isn't an end, or is it just too far away?
Yours endlessly, Kinch Wimpton Janet and who knows how many more...?
MING MING STAR asked Thag the Mathemagician:
In Easy Questions Evil Answers, I love your square root trick, but what do we do about numbers that have an odd number of digits and cannot be split into pairs of digits to start with e.g.144?
For a number such as 144, you just imagine a zero in front so it's 0144. This then splits into pairs of digits 01:44. Now you can do the trick!
Yours rootingly, Thag.
SOMEONE told the Pure Mathematicians:
We just passed the universe's 13,000,000,000th birthday. If we'd had a cake big enough for all the candles it would have needed a top area of 5.2 square kilometers. It would have to be just over 0.59289122 kilometers thick to be self-supporting and if it was cooked at 175įC it would take around 173 days, 31 minutes and 55 seconds to finish cooking.
Wow! That would be enough to feed Porky Boccelli for almost a week!
Yours chompingly, Winch, Kimpton and Janet.
THE HUMAN CALCULATOR told us:
Have you ever noticed that there's a great big PHI Φ symbol right through the middle of a football pitch?
We noticed some very strange things on a football pitch last week, and weren't sure what they were supposed to be doing there. It turns out they were the England team losing 1-4 to Germany.
KAOTOO told us:
Have you heard of the Feynman Point? It's a set of six nines (999999) that appear in PI starting with the 762nd digit.
That is AWESOME. Utterly useless of course , but still awesome all the same!
KEVIN WILSON tells us:
1! + 4! + 5! = 145
Thanks! We love these things.
PYTHAGORAS askes the Pure Mathematicians:
Why does (x3 - x) always divide by 6?
Because x3 - x = x(x2 - 1) = x(x-1)(x+1). One of these elements must be even, and one must divide by 3.
Yours algebraically, Winch, Kimpton and Janet
CURIOUS PERSON asked us:
What is the smallest number to be a square, cube, fourth, fifth, sixth, and seventh?
Either 0 if you count 0, or 1. The next one is 2420 which is a 127 digit number.
RAYBOY tells us:
Here's a multiplication that uses the digits 1-9 once:
1963 x 4= 7852
We love it!
CALCULATOR FREAK asks Professor Fiendish:
What does "LOG" do on a calculator?
"Log" means "logarithm" is usually based on powers of 10. 10 to the power 3 = 1,000 so log(1000) = 3. This is simple for 10,100 1000, 100000 etc, but when you need to know something like "what power of ten do you need to get 5000 ?" you get log(5000) = 3.69897. Before we all had calculators, people used logs to do really complicated sums quickly. It's all very fiendish!
Yours calculatingly, the Prof
COLLIS asked the Pure Mathematicians:
Can you provide a derivation of the general formula for solving quartic polynomials, please?
We had a spare one but it melted on the radiator. Sorry.
Yours carelessly, Winch, Kimpton and Janet.
TERDRAKUS sent Professor Fiendish this great trick!
Multiply any 6 digit number by 3 then 7 then 9 then 11 then 13 then 37. The answer will have 12 digits. If you add the first six digits to the last six, you always get 999,999! E.g. 194673 x3 x7 x9 x11 x13 x37 = 194672805327. Then 194672+ 805327 = 999 999.
That's diabolically brilliant! Thanks!
Yours trickingly, the Prof
EDWARD warns the Evil Gollarks:
I have stuffed your spaceship with golds!!!
P.s. They are actually bombs painted gold.
Eeek, we've been tricked!
Yours panickingly, the Evil Gollarks (but not as evil as Edward!)
ROGER tells the Pure Mathematicians:
Did you know that when you draw any flat figure you can add the dots and spaces together and subtract the number of lines, your answer will always be one. So, D+S-L=1.
Wow! We find this always works so long as we keep all our lines straight.
Yours amazedly, Winch, Kimpton and Janet.
AT&T taught us this neat trick:
Ask a friend to take a secret 4 digit number that has no digit repeating itself (e.g. 4321)
Write it backwards (1234)
Take the smaller number and subtract it from the bigger number (4321-1234 = 3087)
Add the digits together.
Tell your friend the answer is 18! (3+0+8+7 = 18)
Try this trick on your friends, and they'll be surprised that you read their minds!
We LOVE stuff like this - Thanks!
MATHMASTER asks Grizelda The Grisly:
How many arrows do you have?
One less than yesterday because I fired one at Urgum the Axeman when he was bending over today. I couldn't resist it!
Yours cheekily, Grizelda
JOHN from Missouri USA asks The Pure Mathematicians:
Both myself and my son were born on a Friday 13th. What are the chances of this?
There are on average 1.72 Friday 13ths every year. The chance of anyone being born on Friday 13th is 1.72 / 365.25 = 0.0047. The chance of two selected people both being born on Friday 13ths is this number squared which comes to about 0.000022 which is about 1 in 40,000!
ADITYA SEN asks us:
What is the BIGGEST Pythagorean Triplet ever?
There is no limit because any odd number can be the shortest side of a right angled triangle with whole numered side lengths. All will be explained in the "Murderous Maths of Everything" coming out soon!
DAVID RECK asks Titus O'Skinty:
I'm thinking of starting my own gameshow. Can you give me some tips?
Certainly! You must have a game that requires nothing more than guesswork so you can patronise your contestants. You must also insult your audience's intelligence by promoting some drivel known as "cosmic ordering" where you claim that anyone can get anything what they want simply by wishing for it. If people start to get bored of you, quickly mention that you're playing for charity and above all, you must look very pleased with yourself at ALL times.
This is the perfect formula, as demonstrated by Noel Edmonds on "Deal or No Deal".
Yours helpfully, Titus
TINA asks the Pure Mathematicians:
How much is "i" actually worth? Like if you bought something and the storekeeper told you it cost ip, how much are you supposed to pay?
What a great question! As "i" is an imaginary number, it has no normal numerical value. But there again, it might be useful if you were buying something like dreams!
Yours imaginatively, Kimpton Winch and Janet
NATHAN asks Kjartan Poskitt:
How many scarves do you have? Aren't you scared of getting them wet in the bath?
I've got about 20 odd scarves, and yes, they do get wet in the bath unless I keep my rain coat on.
Yours fashionably, Kjartan
JLH tells the Pure Mathematicians:
When numbers are raised to the power of themselves (i.e 4 to the power of 4 = 256) it should have a special name like SQUARETORIAL.
Ha ha, we love it!
Yours happily, Winch Kimpton and Janet.
GYS tells Dolly Snowlips:
Your lips are red not white!
It's not a matter of colour, it's temperature!
Yours coolly, Dolly
BEN YOEL from Thailand asks Kjartan Poskitt:
What time of the day do you write at?
I make notes on scraps of paper anywhere at any time of day, but it's usually late at night when I type it all up. And then next morning I have to correct all the spellings!
Yours typingly, Kjartan
MATHMAN asks Veronica Gumfloss:
If somehow Pongo gets into your house and kisses you when you're asleep, what would you do?
Oh boy.... how could you ASK such a thing .... I don't want to think about it... I'm SO going to be sick...
Yours grossly, Veronica
BRAHM tells Urgum the Axeman:
Your brain is tiny.
What's a brain?
Yours ignorantly, Urgum. YARGHHHH!
COLLIS asks the Pure Mathematicians:
Can you provide a derivation of the general formula for solving quartic polynomials, please?
We had a spare one but it melted on the radiator. Sorry.
Yours carelessly, Winch, Kimpton and Janet
EMMY from Canada asked us:
My friend threw 6 YAHTZEES in one game - what are the chances of that?
We make it about 1 chance in 61,500. Your friend was very lucky!
EUAN tells Riverboat Lil:
I've worked out the least-landed-on- square in Monopoly is Park Lane, because the square seven squares behind it is "go directly to jail" and seven is the most common roll of two dice.
That sounds pretty smart!
Yours winning-second-prize-in-a-beauty-contest-ly, Lil
TEHGEEK asks the Pure Mathematicians:
Is there a quick way of converting hexadecimal to binary. At the moment I just convert the hexadecimal into decimal and then convert that to binary, bit by bit.
You replace each symbol in the hexadecimal to its 4 bit binary equivalent. So "7" in hexa would be 0111 in binary. "B" in hexa would be 1011. So B7 in hexa would be 10110111 and both equal 183 in decimal.
Yours convertingly Winch, Kimpton and Janet.
WORMY keeps asking us why his messages don't get on here and why he doesn't get replies!
Hello Wormy - We do reply but your email address doesn't seem to work!
About half the people who send us messages give an incorrect email address!
IMMY sent us a great idea:
You could have pi as a telephone book. All you need to know is at what position a person's phone number is. pi is a never ending number so it has all number patterns.
AAANNN asks Dolly Snowlips:
What is the most unpopular shape?
The Nofriendsagon. Ho ho!
GILLIAN asks Professor Fiendish:
What is the shape of the universe? My art teacher seems to think it's a 'circle with straight sides'.
Where was your teacher standing when she was looking at it?
Yours doubtfully, The Prof
ZACK BROOKES scared the Pure Mathematicians with this:
If you work out (142/45) - (399,072,549,169,057,923,228,043,079 / 2.5 x 10^29) you get the first 31 digits of PI.
We're just checking that... in our heads of course!
Winch Kimpton and Janet
NICOLA EDE tells us:
17 x 17 x 17 = 4913 and 4+9+1+3 = 17
We love it - thanks Nicola!
GILLIAN asks Professor Fiendish:
What shape is the universe? My art teacher thinks it's a circle with straight sides.
Wow! Where was your teacher standing when he/she saw it?
Yours astronomically The Prof
BANANA MAN tells us:
I have discovered that Skewes' number is NOT 10^10^10^34 (that is just an approximation). Its correct value is e^e^e^79. So there.
That hurts our brains...
KARTIK asks the MAYOR of FASTBUCK
What are the chances of your winning the next mayoral elections?
About 100% give or take a bribe or two.
Yours on expenses-ly, Rudemon Snaffle (Hon)
COLLIS TAHZIB asks The Research Department:
When deriving integration using Rieman sums, can one apply a limit of n -> infinity to radically decrease the f(x) after the interval (x/n) is applied?
Usually, but be sure to do it over the sink in case it bursts.
Yours cautiously, Winch, Kimpton and Janet.
SOFTFLIK asks the Duchess:
Don't you think that your goldfish, Twinkle, is a bit snobby?
That's because she's a goldfish. Wooden fish aren't snobby at all.
Yours classlessly, Lady Fogsworth (Duchess)
SUYOUNG tells the Evil Gollarks:
Now, now, if you step on earth's soil, it have secret sensers in the soil, it will shot the "pi" so you got blasted out of earth! All thankes to my pi shooter.
A PI shooter? We WANT one!
Yours jealously, The Gollarks (evil)
OLIVER told Kjartan Poskitt:
I tossed a coin 100 times. 50 times it landed heads and 50 times it landed tails! Is that strange?
Yes! Fancy tossing a coin 100 times and counting it. VERY strange - you'd make a good Pure Mathematician! Joking aside, the chance is about 8%.
Yours normally, Kjartan
JUSTIN WILLIS told us:
Did you know that (x3 - x) always divides by 6?
No, but we do now! E.g. if x=7 then x3 - x = 343-7=336, and 336 does divide by 6. Brilliant!
Thanks to HANNAH who explains why this works: (x3 - x)=(x-1)x(x+1). In other words you can always make (x3 - x) by multiplying three consecutive numbers together. And any three consecutive numbers has to include one that will divide by 3 and one that will divide by 2, so multipled together the answer will divide by 6.
YUCHEN asked Blade Boccelli:
Why does 1+2=3?
You got a better answer?
Yours interestedly, Blade
LINDA tells us:
If you want to do the square root of 9025 you just cross out the two middle digits to get the answer 95. This also works for 9216
We love this stuff!
DRENCH asks us:
In the tv show Deal or No Deal, what are the odds of knocking out all amounts in order from the Big One down to the dollar and having the smallest amount in your box/briefcase?
Sorry we can't help. We tried to watch it once but as soon as Urgum the Axeman saw Noel Edmond's smug mug he chopped the telly up.
However the MATHINATOR saw this question and contacted us to say the odds are 1/21! (note: 21! = 21x20x19x....3x2x1)
Thanks Mathinator! It saved us having to sit through a show.
JONNY asks Porky
Could you become a little less fat? It ruins my liking for you.
Hey! The more of me there is, the more there is to like.
Yours chompingly, Paul "Porky" Boccelli
THOMAS HIGGINSON tells Dolly Snowlips
I think you are really pretty
So do I.
Yours agreeingly, Dolly x
YOGIE BEAR tells Verinoca Gumfloss:
You have a 1 in 2 chance of going out with Pongo McWhiffy - either you do, or you don't!
Actually it's a 0 in 2 chance. Either I don't or I DO NOT!
Yours oddly, Veronica
ICEBOLT4 tells us:
If you divide 108 by 6, you only need to take away the 0.
and XIAN BIN says:
To divide 105 by 7 take away the 0.
We love sums like this! There are lots more in NUMBERS including: if you want to cancel 16/64 you just cross the 6's out to get 1/4.
MATHS NUTTY asks the Pure Mathematicians:
What's the difference between a pure mathmatician and a normal mathematician?
Pure mathematicians don't need friends or daylight.
Yours in the dark-ly K,W and J.
An MMFAN asks Dolly Snowlips:
Why were the gangsters tortured with your "cake" on Porky Boccelli's birthday in Vicious Circles?
Not tortured. TREATED!
Yours cookingly, Dolly
SWEETPOISON sent us this super message:
Hey! Wassup u ppl? U got a buzin syt eya! Sum of ur pix r mingin but da rest r kul!! Ur gamez r wikid n interesting n hopefuli nex tym i vizit dis syt u'll av new gamez, newe email me kwikli! l8rz!! Peace out! xxxASH n FLOZ wuz eya CHILIN in mafs!xxx hpe u undastand my slang
We all feel 20 years younger now!
KATY asks Kjartan:
In 'Desperate Measures' you said that circles only have one side - but elsewhere it is said that they have infinity sides. What's the truth?
It's ONE curved side or INFINITY straight sides!
Yours countingly, Kjartan
Mr RUSSELL PRICE and YEAR 6 of ST PETER'S SCHOOL, JERSEY tells Professor Fiendish:
In your Diabolical Brainbenders we've found extra solutions to "Ten Tantalising Cards", "Charity Day" and "Megavolt Vaults"!
That's fine. There will be no extra charge.
Yours generously, The Prof
ARTAS asks The Phantom X:
Is there an equation which produces a perfect circle when drawn as a graph?
Oh yes. x2 + y2 = 1 creates a circle of radius 1 around the 0,0 point.
Yours plottingly, X
JELLY asks Pongo McWhiffy:
Why do you like burgers and pants so much? The two don't go together very well.
Now you've got me thinking - the PANTBURGER! Yum!
Yours weirdly, Pongo
KIRSTY asks Dolly Snowlips:
What's your favourite food?
Yours chillily, Dolly.
MATHS ADDICT asks Pythagoras:
In the mail room you signed one message "Ernie" and one "Bertie". Which is your real name?
Ernie is just my nick name.
Yours formally, Bertie Pythagoras
COUNT HOLOK asks the MM editor:
On the brilliant Murderous Maths site you say Philip Reeve is a genius but in the books you say he is evil. Which one is he?
Evil genius - that's him. He's a lovely person, but definitely an evil genius.
Yours in chargely Lulu Moody
REDHAWKER contacted us to say:
Aaaagggrrrhhh!!!! Help!!! I've lost my copy of "More Muderous Maths"!!!!! I'm melting!!! I can't breath! I need...air...
Naturally we're very concerned!
FLAME asks the Pure Mathematicians:
How much is "i" ?
About £3.99 from WH Smiths, but you might get one cheaper at Tescos.
Yours misleadingly, Winch, Kimpton and Janet
ALAN KANAPIN tells the MM author Kjartan:
My Perfect Sausage book contains all the 4 mistakes which are shown on the website!
That's nothing. On my computer I've got the original first draft which is about 400 pages long and it has THOUSANDS of mistakes.
Yours proudly, Kjartan
BANANA MAN asks Riverboat Lil:
In the boardgame of CLUEDO, what are the chances guessing the murderer, the weapon and the room on your first go?
There are 9 rooms, 6 people and 6 weapons so it's 1 in 9x6x6 = 1/324.
Yours with-the-candlestick-in-the-study-ly, Lil
WILL asks the Pure Mathematicians:
How do I become a Pure Mathematician? Do I need to get a degree in Mathematics?
It helps, but having an orange nylon shirt and odd socks is more important.
Yours fashionably, Kinch Kinch and Kinch.
CLOWN challenged us all:
If a*b=c and a+b=c, and a does not equal to b then what are a,b,and c?
Thanks to our consultant MICHAEL JONES who gave us a list of answers...
a=3 b=3/2 c= 9/2 or a=4 b=4/3 c= 16/3 or a = 5 b=5/4 c=25/4 etc.
HUBMAN asks the tall guy in the "mailroom" picture:
Have you noticed that arrow in your hat?
Eh? What? EEEK!
Yours alarmedly, One-Finger Jimmy
QIU ZHE from China tells us:
In China, we call the Pythagorean theorem Gougu theorem. And Pascals triangle is the Jiaxian Triagle after the Chinese inventor. And these inventors invented it hundreds of years before Pascal and Pythagoras.
BANANA MAN asks Pongo:
Where is your burger van?
Next to the municipal rubbish dump. It's rather convenient actually.
Yours aromatically, Pongo
QUIRKY asks "The Gangster in the mailroom picture scratching his head":
Why are you wearing a tie with a picture of a girl wearing a bikini on it?
Shhh....that's my mum!
Yours blushingly, The Weasel
HAZ asks Veronica Gumfloss:
Do you fancy anyone?
Pretty much anyone except Pongo, yes.
Yours fanci-ingly, Veronica
KETURAH tells Pongo McWhiffy:
If you take a bath Veronia might kiss you & if you wear a new suit she might marry you.
Wow! So if I wear a new suit in the bath, that should double my chances!
Yours soggily, Pongo MH asks the Pure Mathematicians:
How can we work out how many zeroes there are in 50! without using a calculator?
Easy - just see how many x5's come up. 5,10,15,20,30,35,40,45 all give you one x5, and 25 and 50 each give two. Total=12 so it should be 12 zeros.
Yours big-numbering-ly, Winch Kimpton and Janet
Csc564deg asks Riverboat Lil:
My copy of The Perfect Sausage has all the flaws. What are the chances of that happening?
About 100% at present! However the second edition due soon should have them all corrected.... Yours accurately, Lil
THOMAS KIPTON O'RIELLY asks Pongo:
Can you send me a takeaway menu, please?
Sorry, my food is so bad I only do THROWAWAY menus.
Yours in Hell's Kitchen-ly Pongo
WORMY tells Truffles the pig:
You're so cute!
It's just an illusion. ANYBODY standing next to Professor Fiendish seems cute compared to him.
Oink oink, Truffles
S F asked Professor Fiendish:
In the Diabolical Book of Brainbenders there is a question about 'The Footskull League'. Do you have the results of any other season?
Sadly not. The owner of the skull wanted it back.
Yours on the touchline, the Prof
LOADS OF PEOPLE SUDDENLY ASKED US:
Find a six digit number where the sum of the digits is 43 and only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000."
Luckily our super-expert MICHAEL JONES proved the only answer is 499,849. You can find out more from Michael at the M-MATHS FORUM!
THE POINTER OUT OF DETAILS asked Dolly Snowlips:
If you don't advocate wearing furs, why do you usually wear a dead mink around your neck?
Dead? Who said it was dead?
Yours offendedly, Dolly
OBB asked us
I got this answer on my calculator screen: 2.2359723 E9 What does it mean?
The E9 means you multiply the 2.2359723 by 109 to get 2,235,972,300. Calculators use the "E" when the screen isn't big enough to show massive or tiny numbers. All is explained in Desperate Measures.
HANNAH WHITAKER tells the Pure Mathematicians:
Here's the most POINTLESS trick in the world:
Pick a number. Add 4. Divide by 2. Now forget all that and say "seven"
WOW! That's truly awesome! But how does it work?
Yours gobsmackedly, Winch and Kimpton
SHUKUUN tells Professor Fiendish:
There once was a v. Fiendish Prof
Who thought he was a mathster boff
He had a pet pig
And a nose very big
And he smells like old cheddar gone off
Oh how lovely! You've made me very proud... The Prof
DAPHNE LEONG from Singapore tells Riverboat Lil:
Hey, guess what? I got a special coin which has tails on both sides!
I've got a coin with tails on three sides. How about that?
Yours strangely, Lil!
POSTMAN PAT asks Veronica Gumfloss:
Where is Pongo's burger bar? It sounds great!
It might sound great, but it smells AWFUL!
Yours nose-holdingly, Vera x
MATHSMASTER asks us:
Please please can we see a close up picture of the new book `The Perfect Sausage and Other Fundamental Formulas'. I think your site rocks and so do your books! Wahoo!!!!!!!!
Wahoo indeed and thanks for your nice message! Here's the Perfect Sausage cover. At the moment Philip Reeve is finishing the pictures inside.
JACK ROBINSON asks the Pure Mathematicians
What shape of cylinder has the biggest volume for the smallest surface area?
Good question! The radius of the base has to be the same as the height of the cylinder - in other words a tin should be twice as wide as it is tall. This means that nearly all normal cans of drink or beans are far too tall. If they were shorter and fatter they would use less metal but hold the same.
GUARTER HOLES asks us:
How often is there a fifth Sunday in February? We had one last year.
Only once every 28 years! The next one will on 29/2/2032.
JOHNNY tells the Pure Mathematicians:
22 + 112 = 102 + 52 = 53 = 125
Yours squaringly, Kinch, Wimpton and Janet.
MATHMAN 1054 sent this great joke to Pongo McWhiffy...
"What did the Buddhist monk say to the burger seller?" - Answer: "Make me one with everything!"
... and when the burger seller took a £10 note, the monk asked "Where's my change?" and the seller replied "Change must come from within!"
Yours sublimely, Pongo
DJFOXY asks the Pure Mathematicians
Why are your names Winch, Kimpton and Janet when there are 4 of you?
4? I can only see three.
Yours confusedly, the other one.
BILLIE LORD points out:
992 =9801 and 98+01=99 Also 2972= 88209 and 88+209=297, are these called Kaprekar numbers?
Yes - and what's more 2973 = 26,198,073 and 26+198+073 = 297!
JONATHAN MUI tells the Pure Mathematicians
September is the 9th month and has 9 letters. Also, 9 September 2009 will be a Wednesday (which also has nine letters).
WOW! We'll have a big party on 9/9/09 to celebrate!
Love and big respect from Kimpton and Winch and Janet
JOHNNY tells us:
Yes - and we've proved it! See Square triangles and cubes
STAR SHINE tells us:
A DECIMAL POINT re-arranges its letters to be, IM A DOT IN PLACE !
We LOVE it! Thanks.
WILLIAM asks Professor Fiendish:
How old are you and when is your birthday?
I'm millions old because I have my birthday EVERY DAY!
Yours blowing-the-candles-ly, the Prof
SMARTMATH asks Pongo:
Do you have a breakfast menu at your burger bar and if not why not?
Somebody ate it.
Yours cookingly, Pongo
ARTAS (and other people) asks Prof. Fiendish:
In the Fiendish Angletron, on pages 74, 75 and 76, why does your black eyepiece keep swapping sides?
I turned around a bit too fast. Now NO MORE questions about my appearance or I'll get very CROSS.
Yours tetchily, Prof Fiendish
POPSY asks Professor Fiendish:
How come in NUMBERS on page 117 you say that you have real teeth, but in the FIENDISH ANGLETRON you do some frustrated gnashing of yellow DENTURES?
ARGHHH! I'm very cross now. For your information I've got teeth AND dentures.
Yours two-faced-ly The Prof
MR BLOBBY gives us this fine piece of useful information:
3/3/3/3/3/3 = 0.01234567901234567901234...
COMMANDO CUCUMBER asks Pongo:
Have you ever considered opening your own fast food stall?
I once left the brakes off on my burger bar and it rolled down the hill VERY fast...
Yours speedily, Pongo
AL gives us this excellent pathetic and useless fact:
TWENTY NINE is the only number that is written with as many strokes as its numerical value! (You need to write Y with 3 strokes)
MATHMAN (we don't know which one because there are LOADS of people who call themselves Mathman) asks Prof Fiendish
Hey prof, why is 1 of your lenses black?
Because if they were both black I wouldn't see anything! Yours obviously, The Prof
Another MATHMAN tells us:
HORRAY, I got lvl 8 on my yr 9 S.A.T.S! And I owe most of it (some to the teacher) to murderous maths. THANKS!
Glad we helped - but if you did well you owe most of it to yourself!
CHARLOTTE asks Pongo Mc Whiffy
Why do you try to kiss Veronica if you know she is going to wallop you?
No pain, no gain...
Yours romantically, Pongo
A special hello to KEVIN who sent us a very funny message from a hotel he was staying in on holiday. He described himself as "a fat boy that wears Harry Potter glasses and has very messy hair, and he wears braces and clothes that say "BE READY 4 THE PI FIGHT IN THE RESTAURANT"!!
GABRIEL asks Riverboat Lil:
How on earth do you do your Mindreading trick? I've never seen anything like it on the computer!
Play the trick a few times - do you see anything in common with the numbers you end up picking?
Yours telepathically, Lil
CLOWN asks us:
How many squares are there on a chessboard? Hint: the answer's not 64!
We happen to know it's 204 (if you make every possible square pattern starting with the one big one measuring 8x8). All this will become clear in the Formulas book next year.
CONNOR and CALUM FORD ask Pongo McWhiffy:
Who was the best burger seller in burger van history?
My Aunt Aroma - you could smell her hot dogs a mile away. What talent.
Yours enviously, Pongo
SAM wished us all a HAPPY PI APPROXIMATION DAY on July 22nd! (22/7)
What a great idea Sam! Next year we'll do something to celebrate...
A MATHSY PERSON tells the Pure Mathematicians:
As a circle has one side, shouldn't it be called a UNAGON?
Wow! Now there's a thought... Wimpton Kinch and the other one
A MATHSY PERSON also asked:
Are there any whole numbers so that a2 + a2 = b2 ?
No because you get 2a2=b2 therefore (SQRT2) x a = b and SQRT2 is irrational.
SAKI asks Grizelda the Grisly:
How's your scalp collection going?
Not well. The last scalp I got was Kjartan Poskitt and he's bald. Yuk.
Yours barbarically, Grizelda.
ALOHA asks the Pure Mathematicians:
Which one of you is Winch, which is Kimpton and which one is Janet?
I'm WInch and the others are over there.
Yours introducingly, Winch.
POPSY from NZ tells us:
The highest score I got on the profs' SNAKE GAME in NO FEAR mode was 27740. By then my snake was looking like a boa constrictor.
That is AMAZING! Our best score on fast is about 11½
S MURRAY asks the gangsters:
Did you actually read the newspaper on page 120 of Phantom X? It has wonderful articles such as "Fat? Bald? Smelly? Ha ha!" and "Poskitt voted God" and even a message to bored readers: "Only 40 pages to go!".
Wow! We better look again... Blade.
NICHOLAS asks Professor Fiendish
What's the millionth digit of pi?
It's a 1.
Yours smugly, The Prof...
LALA asks Pongo McWhiffy:
What would you do if Veronica Gumfloss liked your burgers and kissed you every time you gave her one?
Yours woozily, Pongo
Thanks to LAURA for this brilliant joke...
There are 10 types of people in the world:
those who understand binary, and those who don't.
Ho ho ho!
STAR SHINE asks Professor Fiendish's Fridge:
How do you cope? I'd die at the first whiff of what Prof. Fiendish puts in you!
It's better being the fridge than the bath - he puts himself in that! (Very occasionally).
Yours coolly - the Fiendish Fridge
SUPERTOM asks Ug and Blagga (from The Essential Arithmetricks)
What happened to the pterochicks?
They are all live and well and laying ptero-eggs
Yours neanderthally, Ug and Blagga
MULLET asks us:
On dice, why are the numbers 1-6, why not 10-16?
Because 10-16 would need a seven sided dice!
SUPERTOM asks Pongo McWhiffy:
Does this flavour of burger sound good- rhubarb and custard?
It sounds great -especially with onions!
Yours from Hells-Kitchenly, Pongo
THE ALIEN AXE asks Pongo McWhiffy:
Is it possible to reconstruct all infinity contangent spaces such as Selmer groups to a higher degree of accuracy?
Er... yes! And did you want onions and ketchup on that?
Yours from the burger van, Pongo
JAMES asks Primrose Poppet:
Not meaning to be rude or anything, but how old are you?
More than a May fly, less than a tree. And thank you for my first ever email message!
Yours tweelly-gumdrops, Primrose
CHENGY asks the Pure Mathematicians:
Does i5 = i ?
We think so. Good one!
Yours imaginatively, Winch and the others
SHEEP asks Pythagoras:
Are you our maths teacher because my friend and I reckon you are. He seems to know everything about you, and he knows that you are an inquisitive little chappie.
I've been dead 2000 years. Is this like your maths teacher?
Yours from the grave... Ernie Pythagoras
BOFF asks Kjartan Poskitt:
Is that your real name? And I do not not want any funny answers.
Yours completely humourlessly, Kjartan Poskitt.
JOE SYMONS-SMYTH asks Philip Reeve:
In your new book, "Predator's Gold", one of the gods people pray to is called "Poskitt". Is there just a hint of bribery going on here?
Not bribery. It's hero worship.
Yours artistically, Mr Reeve.
JORDAN asks The Pure Mathematicians:
I've just read the preveiw of The Fiendish Angletron and it looks great! But, why do you want a slide that can go into the duck pond?
Aha! It's a secret... but all will be revealed when the book comes out!
Yours mysteriously Winch, Kimpton and Janet.
GAIL WEISS asks Dolly Snowlips:
How do you walk in such high heels?????????????????????????
I don't walk Honey, I glide...
Yrs smoothly, Dolly
MARTIN BIDDLE asks us:
I read your formula for the area of a regular polygon in the research lab but didn't understand the TAN bit. What does it mean?
Aha! All is explained in The Fiendish Angletron
DW asks Riverboat Lil:
What are the chances of having a random 365 people who all have different birthdays?
It's 365!/365365 = 0.0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000145495 5215618703 4033714016 %
In other words it's pretty small!
Yours accurately... Lil
CARSON KRESSLEY tells Veronica Gumfloss:
I'll give you a million dollars for just one kiss!
Wow! What do I get for a hug too?
Yours already-puckered-up... Veronica
MOI tells the Pure Mathematicians:
In the books they show 4 of you, but in your messages only 3 of you sign.
Wow! Is there really four of us? We were always too busy doing posh sums to count ourselves.
Yours amazedly, Winch, Kimpton, Janet and ?
INNOCENT asks us all:
What will the governing equation of motion for a thin plate oscillating in a fluid medium be like? (as in how will the 2-dimensional wave equation look like with the viscous drag on the fluid medium?)
It will be pretty gruesome. That's what it will be like.
MEG asks Veronica Gumfloss:
How many times has Pongo McWhiffy asked you to go out with him?
Exactly the same number of times as I've said NO.
Yours unavailably... Veronica
I discovered that in the Fibonacci series 144 is the twelfth number and it's also twelve squared!
How utterly useless. We LOVE it!
REBECCA asks Dolly Snowlips:
Did you really help the gangsters escape jail in More Murderous Maths ?
Shhhh - it's something I don't like to admit!
Yours embarassedly, Dolly.
TOMATH asks the Pure Mathematicians:
What is a PARSEC?
It's a space measurement and equals about 3.26 light years or 31,000,000,000,000km. It's all explained in "The Fiendish Angletron" book coming out soon, along with our secret identities!
Wahey! - Winch and Kimpton
BOB asks Luigi:
Is is scary when the Gabriannis and the Boccellis try to get along in your diner?
I dunno - it's never lasted long enough for me to tell.
Yours ducked down behind the counterly, Luigi
JAKE asks us:
153 is equal to the sum of the cube of its digits (13+53+33 = 1+125+27 = 153). Are there any other numbers like this?
Oh yes - 370, 371 and 407. They're all in the NUMBERS book.
"F+V-E=2" asks Truffles (Professor Fiendish's pet pig):
Why oh why does the Prof own a pig?
To make his house smell better.
Oink oink.... Truffles
REHAN REX asks the Pure Mathematicinas:
Could black holes act as giant particle accelerators and twist particles into dark matter and dark energy?
We built a machine to try it but one of the the wheels fell off so we never found out.
Yours uncertainly, Kinch, Wimpton and Janet
VIC asks us:
What is the highest times tables someone has read up to?
We don't know, but we can tell you that people in casinos have to know the 35 times table. (Which is one good reason to avoid casinos!)
SAM GIBBON tells The Pure Mathematicians:
In the Research Lab, one question says "What does 0/0 equal?". But in The Phantom X book, rule 5 says that dividing by zero is not allowed!
You're right, in algebra, you're not allowed to divide by zero, but that doesn't stop people wondering what happens when you do!
Yours law-abidingly, Winch, Kimpton and Janet
DAVID tells Kjartan Poskitt:
It's giving me so much grief trying to make a triflexagon!
They used to give me grief too! Make sure you're folding it right - the first fold goes "in" and the second goes "out" - look at the instructions very carefully.
Good Luck! Kjartan
RHIANNA G-T tells Professor Fiendish:
Last time I played your Diabolical Dots I scored 41 and you got 8.
Bah! But I bet I'll beat you on Grub Squish!"
Yours competitively, the Prof
LUKE asks Veronica Gumfloss:
What is infinity written in natural numbers?
Whad'ya ask me for? My speciality is natural beauty which in my case IS infinite.
Yours modestly, Veronica xx
KITY KAT tells us:
I find algebra really hard and I have just started high school. Does anyone else?
Cheer up Kity - almost EVERYONE finds algebra hard. Have you tried looking at The Phantom X ?
Good luck... you're not alone!
ALEX JEFFREYS asks us:
How often does Friday 13th occur? And how often do you get a BLUE MOON? (i.e. a second full moon in the same month. July 2004 will have one.)
Friday 13th comes 48 times in 28 years. Blue Moons about 7 times in every 19 years or about once in 33 months.
RHIANNA G-T tells Professor Fiendish:
HA HA! HA HA! HA HA! HA HA!HA HA! I know a way out of your Room of Doom and it's not even a hidden link!
Turning the computer off usually works for most people!
Har har - The Prof
STIG asks Pythagoras:
Why are you such a loser, you make us study this pointless theorem but what does it actually mean?
Hey! When I have to study a theorem of yours THEN I'll think I'm a loser!
Yours hypotenusingly - Bertie Pythagoras
NOAH asks the author:
Is there really a book called The Fiendish Angletron?
There will be! Look at our books page.
Best wishes, Kjartan
LOLLI tells the Pure Mathematicians:
I can prove that 0.999 recurring (or 0.999...)= 1.
Let 0.999... = x
10x = 9.999...
10x - x = 9.999... - 0.999... = 9
So 9x=9 therefore x = 1.
Therefore 0.999... = 1.
WE LOVE IT!
Yrs impressedly, Kimpton and Winch and Janet.
MOI asked us:
Is there an EXACT number of combinations for a Rubik's cube?
Oh yes. Brace yourself - according to the brilliant David Singmaster the number of combinations is worked out from (8! x 12! / 2 ) x (38/3) x 212/2 and this becomes 227314537211 = 43,252,003,274,489,856,000
If a computer could count 1000 patterns per second, it would take about 1.4 million years to count them all...
... after the above message appeared we heard from MATHMAN:
I'm afraid 1.4 billion is just not accurate enough. You should be ashamed of yourselves. It's:
JOE SYMONS-SMYTH told us:
If half empty really is the same as half full, then 1/2F=1/2E and therefore F=E. So actually, an empty glass has the same amount in it as a full one! ...
...but then JESSIE B.C. said:
There is no such thing as half empty or half full. The glass is simply twice as large as it needs to be. Makes sense to us!
...and then STEVEN CHARLTON said:
Empty and Full are two different measures so you shouldn't use them together in an algebra equation. Clever!
HRETHEL asked the Pure Mathematicans:
What is the inverse of a right-angled portly triangle?
An elliptical cube, obviously.
Yours twistedly, Winch Wicnh Wnich and Wchin.
JONATHAN MUI asks "The Chevy from Do You Feel Lucky?"
What ARE you going to do with all those pants you won playing dice?
Aha! Keep your eye on this !
Keep it close to your chest - The Chevy
DANIEL sent us this neat limerick:
A dozen, a gross and a score
Add three times the square root of four
Divided by seven
Add five times eleven
Is nine squared and not a bit more
In other words: (12+144+20 + 3x2)/7 +55 =81
Good one Daniel!
BUB asks Half-Smile Gabrianni:
Why is your mouth half a smile?
Because I'm saving half a joke for my old age.
Keep it easy, Half-Smile.
SUNNY from Slovenia tells us:
Did you know that in the seventh Murderous Maths book on page 77 is a seven-sided shape?
NICK asks the Pure Mathematicians:
What is an OCTILLION?
If a billion is 1,000,000,000 (which is the US standard) then an octillion is 1 with 27 zeros.
Yours countingly, Winch Kimpton and Janet.
LIL MISS MAGIC tells us:
ur books are gr8! my m8z started readin them and now they talk about them not about boyz!
Thnx a 1,000,000 :-) !
JORDAN asks "anyone who knows":
Why is one of the ways to solve a quadratics equation called 'Completing The Square'?
Have a look at our completing the square page. Hope that helps!
Yours ... someone who thinks she knows.
JESSIE B. C. asks Dolly Snowlips:
Why are you called Snowlips if your lips are really bright red? I don't know of any red snow.
You should have seen the snow outside Luigi's diner last New Years Eve after the gangsters had been arguing over the bill!
Yours coolly, Dolly
HTAMMATH asks EVERYONE...
Please buy The Phantom X. It will make enough money to allow Kjartan Poskitt to give up his day job as a dustbin man and write more wonderful books quicker. Thank you
Hmmm, we think he's more use as a dustbin man!
SYMB tells the cameraman filming K P:
You don't exist! The fly keeps on doing the same thing!
Actually there's TWO flies, and his finger twitches! Look closely (but boy, it's boring).
Yours filmingly, Smudge Gibson, the Camerman.
SOLOTAMEEKU asks Dolly Snowlips:
What kind of fur is your coat made from? I think it looks like cheetah fur but my friend thinks its albino yeti fur.
It's neither because I don't believe in endangering any species apart from useless men. The fur actually comes from the mould on a 10 year old cheese sandwich.
Yours smelling-attractive-to-micely, Dolly.
JORDAN asks The Phantom X:
Why, oh why are you called Xylophone? Did your parents go crazy?
No. My parents are the Phantom T and the Phantom B, known as Tuba and Bagpipes to their friends.
Yours from the shadows... The Phantom.
DISGUSTED tells everyone:
Honestly, don't people realise that there is one sad person writing all these books, and none of the characters are real? HONESTLY!
Careful! If you really believe that then Santa Claus won't bring you any Christmas presents.
TOMATH asks the Pure Mathematicians:
What are the Landau-Ramanujan constant, the Twin prime constant, Artin's constant, Mertens constant M and Catalan's constant?
Dunno, but they sound great! What are they then?
Yours keenly, Winch, winch, Winch, Kimpton and Janet.
OSNAT KATZ asks Professor Fiendish:
Hey Proffo! Can you PRETTY PLEASE install a 'Summon the Professor' button (like in The Phantom X) under my desk at Sunnyfields School?
Er... but I might get summoned in a geography lesson! Eeeek!
Yours nervously, The Prof
ALISTAIR LYNN suggests:
Why don't you measure intelligence in Poskitts? IQ of 20 = 1 Poskitt etc etc...
That doesn't work because I'd have an IQ of about 11 Poskitts
Yours intelligently, Kjartan Poskitt.
JERRY FUNG asks Professor Fiendish:
I found your first name in the ROOM OF DOOM. But doesn't it also appear in one of the MM books?
Well spotted! Yes, my first name appears rather subtlely in the greatest book ever written which is brilliant.
Har har, The Prof
SOL PACHNER asks the Pure Mathematicians:
((((pi^phi)/e)*2)/phi)/e = 1
Am I right?
But then Sol sent this message:
Sorry! I meant (((((pi^phi) / e) / e) * 2) / phi) / (((((pi^phi) / e) * 2) / phi) / e) = 1
Phew! Thank goodness you got that all sorted out.
Yours relievedly, Wimp Wimp and Wimp.
TOMATH tells the Pure Mathematicians:
Your TETRIS game is wicked! Are you going to inserting any more entertainment of this greatness into this fine online mathematical assistance outlet?
We'll do our best!
Yours blushingly, Winch, Winch, Janet and Winch.
SOME GUY ON THE INTERNET tells Professor Fiendish:
Hey! I got out of your room of doom, I've found every secret page on the site, MwaHaHaHa! I am evolving into pure energy!
Sounds more like your battery's gone flat to me.
Yours mwahahaha-ingly back, The Prof.
THE MATHINATOR asks The Pure Mathematicians:
What are Napiers Bones?
They are a neat old way of doing multiplication. We might put it in the reseach lab one day!
Yours multiplyingly, Kimpton, Winch and Janet.
MATH MAN tells The Pure Mathematicians:
The Great Pyramid of Khufu - if you divide its height by half its perimeter you get PI to 15 decimal places.
We love this stuff! More more more please!
Yours hungrily, Wimpton, Kincht and Janet.
MICK asks us:
How many microns in a milimetre?
There are 1000 microns and two letter "l"s.
Yours slightly smugly, the MM computer and spell checker.
LUKE JONES asks Half-Smile Gabrianni:
Tell me the EXACT value of pi.
Exactly three and a bit.
Yours accurately, Half-Smile.
UGRID asks the Pure Mathematicians:
What's the Riemann Zeta Fuction?
It's very similar to the Riemann Zeta Function but it has an "n" missing.
Yours cleverly, Kinch, Wimpton and Janet.
JORDAN asks NUMBERS:
How did you get so good at maths?
When I was still inside my mum she ate a phone directory.
Yours calculatingly, Numbers.
BECCI asks the peasant captured by the troll in More Murderous Maths:
Has anyone ever fallen on top of you or the troll when they have fallen down the hole, or are you the only wally that fell down it?
I'm the only one. But thanks for worrying about me. I bet you're the only MM reader who even noticed me.
Yours abandonedly, Armitage Tuke. (the peasant)
ADAM the TAYLOR sent this odd rhyme in!
"Eleven eleven" so you won't be confused
has nothing to do with odd bases
It's simply ten thousand that's multiplied by
one ninth to four decimal places.
Good one Adam!
JOE SYMONS-SMYTH also asks the Maths Monk
What does your face look like? Are you a man or a woman or neither or both?
I dunno what I look like because I don't have a reflection in mirrors. But whatever I am I'm sure I'm utterly gorgeous.
Keep it rational, The Monk
ALISTAIR LYNN asks the Pure Mathematicians
If you took the decimal point out of pi and added up all the digits, what would the digital root be?
That's a bit like asking: "if you listened to every noise in the world at once, what colour would it be?" We think the answer is brown to both questions.
Yrs researchingly, Kimpton and Winch
MICHAEL WALLIS asks Professor Fiendish:
How come you've never heard of Kjartan Poskitt when he created you?
Because he created me when I wasn't looking. He's very sneaky like that.... whoever he is.
Yrs diabolically, The Prof.
MASTER OF ARTS AND SCIENCES asks Professor Fiendish:
How come I found so many grammar mistakes in your Diabolical Brainbenders?
Because you're obviously a rather boring person who had given up trying to solve any of the puzzles! Besides, perfect grammar is only for job applications and camera instructions. It kills the soul of great literature. Good reply eh? Do feel free to show it to any English teachers you know.
Yours smugly, Prof F.
PENNY asks Pongo:
Pant Racing is good, but why don't you race something else?
Oh, nothing else has quite the same atmosphere as pant racing. Trust me.
Yours whiffingly, Pongo
JANG MENG from Kuala Lumpur asks Truffles:
Can you help me with the Devil's Dice in Diabolical Brainbenders? I've been working it out for 3 weeks!
Ah... sorry about that! You must have got one of the faulty copies. Check Devils Dice Help !
Oink oink, Truffles
ELIZABETH asks Pongo McWhiffy:
How do your pants move in your pants race?
They are being chased by my socks.
Yours aromatically, Pongo
THE JOHN KNOWN AS JOHN asks the Pure Mathematicians:
Can you tell me what "Graham's Number" is?
We certainly can. It's big. Very big. To give you a clue - if you took the whole universe apart atom by atom, then rearranged all the atoms in as many different ways as possible... it's a lot bigger than the number of ways. Like we said: BIG.
Yours droolingly, Winchton and Kimpt
DANIEL WRIGHT asks The Great Rhun: Where did you get the Ghingi from? I'd like one.
It just followed me down the street one day. Then it followed me home, then into the bathroom. Trust me, you DON'T want one.
Yours magnificently, the Rhun
JESSIE BRECHIN asks the Pure Mathematicians: What's so funny about a telephone book?
Haven't you realised? All the numbers are in the wrong order!! They should start 000001 then 000002 and so on. It's a scream!
Yours chucklingly, Winch and Kimpton
NC impressed everybody by telling the Gollarks: Why do you want the Earth so much? Anyway we don't mind sharing, but you should learn about Earth first!
It's small, round and has splashy bits. What's to learn?
Yours slightly humbledly, the Gollarks
CAMILLA JONES asks Veronica: Hi I go to St Swithuns school and at the moment I am doing my exams and I have a maths one coming up so could you give me a few tips?
Use a pen or pencil to write your answers and NOT a lipstick which would be very stoooopid and the only marks you get are all over your sleeve. The teachers don't actually tell you that, but take it from me, it's true.
Big love to you and Sarah H and all your other friends - Veronica
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