The TEN DIGIT Teaser
It's a simple enough question:
Can you form a tendigit number using each digit once so that...
 the first digit on its own divides by 1
 the first two digits on their own divide by 2
 the first three digits on their own divide by 3
 the first four digits on their own divide by 4
... and so on until...
 the first nine digits on their own divide by 9
 the complete ten digit number divides by 10?
?
Suppose your answer was 7234619850
7 divides by 1, so that's ok.
72 divides by 2
723 divides by 3
7234 ... doesn't divide by 4, so it's no good!
The really neat thing is that there is only ONE possible answer!
To do this you'll need the dividing tests.
When does a number divide by 110? 
1/  Anything divides by 1

2/  Number must be even (ending 2,4,6,8,0)

3/  Add the digits in the number. If the answer divides by 3, so does the number.

4/  The last two digits must divide by 4. To test: if the secondlast digit is odd, the last digit must be 2 or 6. If the secondlast digit is even, the last digit must be 0,4 or 8.

5/  Last digit must be 0 or 5.

6/  Number must be even and divide by 3.

7/  Remove last digit, and multiply it by 2. Subtract from other digits. Answer must be 0 or divide by 7. E.g. 623: remove 3 and x2 = 6. 626 = 56 which divides by 7, so does 623.

8/  The last three digits must divide by 8. To test: if the thirdlast digit is even, the last two digits must divide by 8. If the thirdlast last digit is odd, last two digits must divide by 4, but NOT 8.

9/  Add the digits in the number. If the answer divides by 9, so does the number.

10/  There's a 0 on the end.

Stuck? Then click on our Pure Mathematicians for the answer!
