Modular arithmetic

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.

Can you interpret this algorithm to determine the day on which you were born?

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

What is the remainder when 2^{164}is divided by 7?

What is the units digit for the number 123^(456) ?

Find and explain a short and neat proof that 5^(2n+1) + 11^(2n+1) + 17^(2n+1) is divisible by 33 for every non negative integer n.

What day of the week were you born on? Do you know? Here's a way to find out.