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Archive for September, 2011

## And the first last shall be first…

Posted by Karl Sharman under Tom (15 Responds)

Find integers where multiplying them by single digits (2-9) “rotates” their digits one position, so that the last digit become the first digit.
I’ll give you the first one, just to show how easy it is…
105263157894736842 * 2 = 210526315789473684

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## Maths challenge 14

Posted by Chris under MathsChallenge (5 Responds)

1. Prove that n^2 + 2 is not divisible by 4 for any integer n.
2. Prove that n^3 – n is divisible by 24 for any odd integer n.
3. Prove that n^2 – 1 is divisible by 8 when n is odd.
4. Prove that n^5 – n is divisible by 30 for any integer n.
This [...]

## Maths challenge 13

Posted by Chris under MathsChallenge (18 Responds)

I’m sure this one’s easy, but it looks nice:
1 = 1²
1+2+1 = 2²
1+2+3+2+1 = 3²
1+2+3+4+3+2+1 = 4²
etc.
show that 1+2+3+…+n+…3+2+1 = n²

## Maths challenge 12

Posted by Chris under MathsChallenge (11 Responds)

Prove that the iterative sum of the digits of the square of any integer > 0 is 1,4,7 or 9.
e.g. 89² = 7921, 7+2+9+1 = 19, 1+9 = 10, 1+0 = 1.
I hope this isn’t trivial (or mega hard).

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