MURDEROUS MATHS BRAINBENDERS
Here are a mixture of puzzles sent in by some of our regular visitors.
Go on  give them a try!
ANSWERS are given at the bottom of the page.

THE LUCKY SUM

HU YI JIE of Singapore sent us this quaint little sum:


Can you substitute a digit for each letter so that the sum works?





THE KINGS MOVE
Moving one square at a time either to the right, down or diagonally down/right, how many ways can the KING reach the QUEEN?
Hint: there are 3 ways he can reach the Jack and 7 ways to reach each Bishop

CLOCK WORK
18:41:53 27/06
A clock shows the time and date in the HH:MM:SS DD/MM format as seen here.
Using all the digits 09 once, what is the earliest time and date the clock can show? And the latest?





THE SEVEN SQUARES by Frankie
There are 28 spots here.
Can you connect the spots with straight lines to make seven squares?
You may not use any spot more than once.
You might like to RIGHT CLICK on the image and then print it out!




THE AREA OF THE ANULUS by Alex Jeffreys
An anulus is the red part of this shape. (It's like a disc with a hole in it.)
Amazingly enough you can work out the area of the anulus... only using ONE measurement!
Can you see which measurement you should take and work out the formula?




O and X's
This is another tough challenge from HU YI JIE!


Can you divide this grid into four areas that are exactly the same size and shape...
but each shape MUST contain one X and one O ?




The Midnight Train
SEUNGYUN JEE challenged us with this tricky situation:
The four Gabrianni brothers have 17 minutes to catch the midnight train out of town.
To reach the station they must all cross a narrow bridge BUT...
it's dark, they only have one torch and the bridge can only carry a maximum of TWO
people at once.
Any person or couple crossing the bridge MUST have the torch with them.
The torch must be carried across, it cannot be thrown.
Each brother walks at a different speed and a pair must walk together at the rate of the slower man's pace.
 Chainsaw Charlie: 1 minute to cross
 Numbers: 2 minutes to cross
 HalfSmile: 5 minutes to cross
 Weasel: 10 minutes to cross (because they made him carry all the cases.)
For example: If Chainsaw and Weasel cross first it will take 10 minutes. If Weasel
comes back with the torch, that's 20 minutes gone and they missed the train!
So can you help them reach the train on time?



Stuck? Then remember that the ANSWERS are given at the bottom of the page.



THE COIN SYSTEM
In the principality of Potluck, the currency is the Fluke which is worth
100 Jammies. The Bank of Potluck has just issued the new One Fluke note, but
now want a coin system for the Jammies. The plan is that you should be able to
make ANY amount between 1 and 100 Jammies by using just one or two coins.
(The two coins can be the same or different.)
What is the smallest number
of different coins they need for their new system  and what are they?

WHEN TIME GOES BACKWARDS!
ADAM DAVIES made us think about this:
Two minutes past 8pm on Dec 21st 2002 reads as
20.02 21.12 2002
So when's the NEXT time and date that has digits that read the same
backwards as forwards?




Substitute a digit for each letter so that these sums work.




CORRECTION
62  63 = 1
Obviously this sum is wrong, but it gives us two challenges:
EASY: can you make this sum work by moving one little line?
TOUGH: can you make it work by moving one digit?

FOUR SIMPLE SUMS
BELIAL asks: Can you replace the letters ai with the digits 19 so that
all four sums are correct?

WHICH IS BIGGER?



THE GHINJI'S CAGE
ADAM TAYLOR tells us about the cage in which the Great Rhun of Jepatti keeps his
three tongued monster. The cage door has several different locks, and it can only be opened if every lock is undone.
The Grand Cahjoon and four slaves are in charge
of guarding the door, but the Rhun has given out the keys in such a way that the Grand
Cahjoon can only unlock the door if (any) one of the slaves is with him. The slaves
can only unlock the door if at least three of them work together.
What was the smallest number of locks needed for the door?




THE DRY POTATOES
Carl Turner says:
You have a 100kg sack of potatoes, but 99% of it is water.
You leave it out in the hot sun and when you come back, only 98% of the sack's contents is now water due to evaporation.
So how much does the sack now weigh?
Take a quick guess, then carefully check it. You might be surprised!



Give up? Don't forget: ANSWERS are given at the bottom of the page.
THE WINE BOTTLES!
JAMIE WALLHEAD sent this amazing problem into our Research Lab.
It completely foxed us, but luckily a couple of MM fans did get an answer!
A wine importer received a large consignment of bottles of
wine from his favourite French vineyard.
 He immediately celebrated by
drinking one of the bottles.
 The day after receiving the wine he sold
exactly a fifth of the remaining bottles, which was a good enough excuse
to treat himself to a second bottle.
 On the third day he again sold exactly one fifth of the bottles he had in stock
at the beginning of the day. So again he celebrated with a bottle for
himself.
 This pattern continued until the end of the seventh day, when the
number of bottles left no longer made it possible for him to dispose of a
fifth of them on the eighth day.
How many bottles did the wine importer have when he started?
If you think this puzzle is too
Murderous to tackle, you'll be amazed to know that it had only been on site for 12 hours
when we got our first solution from Jenny Wood which she worked out with a pencil and paper!
A day later we got another (smaller) answer from Carl Turner who used a spreadsheet
(ingenious). Their answers are given in the box below ... but we warn you,
they are both higher than 10,000!
We would also like to thank John McGuinness, a jovial gentleman of Whitby who came up with a wonderful (but impossible) answer: he starts with minus four bottles! When he drinks one he has minus five, then he sells a fifth of 5 which is 1 so he gets back to 4 again.



FIVE VOWELS
ADAM TAYLOR asks:
What number, when written out in English contains all five vowels (a,e,i,o,u) and has
no repeated letters?

THE 3 and 5 LITRE JARS
"S8" reminded us of this classic old puzzle:
I have two jars, one holds 3 litres and the other holds 5. How can I go to the stream
and come back with exactly 4 litres of water?



EXTRA MONEY!
JAY KIM sent us this classic:
Here are 7 coins in a cross. There are 3 coins in the vertical line and
five coins in the horizontal line. Can you move the coins so that there
are five coins in both horizontal AND vertical lines?

0
0 0 0 0 0
0


THE FOUR TRIANGLES
Lord Jay asks:
Can you arrange 6 matches to make FOUR equilateral triangles?




ANSWERS!
LUCKY SUM:
57 + 870 + 9441 = 10368
O and X's:
The pattern of "H"s shows the shape of each piece
KINGS MOVE:
63 ways
CLOCK WORK
17:48:59 26/03 and 17:56:43 28/09
MIDNIGHT TRAIN:
Charlie and Numbers go across (2mins)
Charlie comes back (1min).
HalfSmile and Weasel go across (10 mins)
Numbers comes back (2mins)
Charlie and Numbers go across (2mins).
Total time= 17 mins!
THE COIN SYSTEM:
They need 16 different types of coin:
1, 3, 4, 9, 11, 16, 20, 25, 30, 34, 39, 41, 46, 47, 49, 50
WHEN TIME GOES BACKWARDS:
Two minutes past one in the morning of Jan 10th 2010:
01.02 10.01 2010
THE MAGIC SUM:
92836 + 12836= 105672
DEVIOUS:
6713298 x 8 = 53706384
CORRECTION:
EASY: 62 = 63 1 TOUGH: 2^{6}  63 = 1
WHICH IS BIGGER?:
They're both the same! If you square them both, they both come to 27/8
FOUR SIMPLE SUMS:
a=9 b=5 c=4 d=6 e=3 f=2 g=1 h=7 i=8
THE GHINJI'S CAGE:
There were seven locks labelled ABCDEFG.
The Grand Cahoon had keys ABCDEF.
The slaves had keys
ABCG ADEG BDFG CEFG
THE DRY POTATOES:
50 kg. (Amazing but true!)
THE WINE BOTTLES:
Jenny's answer was 31,246 and Carl's answer was 15,621.
Mengqi Li from China found that 78,121 also works, but we think Carl's answer is the smallest possible.
Someone called Johnny then told us that Mengqi Li's 78,121 also works on day 8 and that 46,871 and 62,496 both work!
FIVE VOWELS:
5,000  five thousand.
3 AND 5 LITRE JARS:
Fill the 3, empty into 5. Fill the 3, top up the five. (This leaves 1 litre
in the 3). Empty out the 5. Pour the 1 litre from the 3 into the 5.
Fill the 3, then bring both jars home!
EXTRA MONEY:
Take the two coins at each end of the horizontal line and put them ON TOP
of the middle coin!
FOUR TRIANGLES:
Arrange 3 matches in an equilateral triangle on a flat surface, then use the other three to
complete a pyramid.
THE ODD MISTAKE:
Didn't you see it? Then just read the question again slowly, out loud!
SEVEN SQUARES:

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