Working systematically

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

How many ways are there to make 11p using 1p, 2p and 5p coins?

Can you work out the values of the digits in this addition sum?

How many different flags can you make?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Can you solve this magic square?