## 6 digit square

Find any/all 6 digit numbers that are squares. The catch is, that the last 3 digits is 1 more than the first 3 digits. e.g. the number might look like 123124 (but that isn’t a square).

If there aren’t any such numbers, prove it.

Archive for January, 2014

Posted by Chris under MathsChallenge (7 Responds)

Find any/all 6 digit numbers that are squares. The catch is, that the last 3 digits is 1 more than the first 3 digits. e.g. the number might look like 123124 (but that isn’t a square).

If there aren’t any such numbers, prove it.

Posted by Chris under MathsChallenge (33 Responds)

I have four children. Their ages (a whole number of years) are between 2 and 16 inclusive. No two have the same age. Last year, the square of the age of the oldest was the same as the sum of the squares of the ages of the other three. Next year the sum of the [...]

Posted by Chris under MathsChallenge (11 Responds)

Find four distinct positive integers such that their product is divisible by the sum of each pair of them.

If that isn’t hard enough, can you do the same with five numbers?

Warning – this might be another stinker.

Posted by Chris under MathsChallenge (23 Responds)

The seven dwarfs decide that they want to line up in alternating height order.

i.e. going from left to right they want to be in the order Hi-Lo-Hi-Lo-Hi-Lo-Hi.

How many ways can they do that?

What if Snow White is included?

Assume no two have exactly the same height.

Posted by Chris under MathsChallenge (9 Responds)

34! = 295 232 799 dc9 604 140 847 618 609 643 5ba 000 000

That’s 34 factorial = 34 * 33 * 32 *…* 3 * 2 * 1

Find a, b, c and d by “clever” arguments. i.e. don’t just bung it into a massive calculator.

Posted by Chris under MathsChallenge (6 Responds)

Fourteen years late but easy, prove that 121n – 25n + 1900n – (-4)n is divisible by 2000