Purr-fection

What is the smallest perfect square that ends with the four digits 9009?

Exhaustion

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Difference Dynamics

Age 14 to 18 Challenge Level:

 Choose any three numbers. The differences between your numbers give you three new numbers. Repeat this operation to give a sequence. In this example the sequence starts: $15, 39, 8 \to 24, 31, 7 \to 7, 24, 17 \to 17, 7, 10 ...$. What happens to this sequence. Investigate for different starting points.

What do you notice? Can you explain what happens?

How about sequences starting with four numbers, or two numbers?

See the article Difference Dynamics Discussion.