Working systematically

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

This grid can be filled so that each of the numbers 1, 2, 3, 4, 5 appears just once in each row, column and diagonal. Which number goes in the centre square?

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?

Weekly Problem 11 - 2011
Kanga hops ten times in one of four directions. At how many different points can he end up?

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?

How many different phone numbers are there starting with a 3 and with at most two different digits?

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?