Working systematically

problem
One out one under

Age

14 to 16

Challenge level

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?
problem
T for tan

Age

16 to 18

Challenge level

Can you find a way to prove the trig identities using a diagram?
problem
9 weights

Age

11 to 14

Challenge level

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?
problem
Spotting the loophole

Age

14 to 16

Challenge level

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?
problem
Train routes

Age

5 to 7

Challenge level

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?
problem
Simple train journeys

Age

5 to 11

Challenge level

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?
problem
Quadruple Sudoku

Age

11 to 16

Challenge level

Four small numbers give the clue to the contents of the four surrounding cells.
problem
The great weights puzzle

Age

14 to 16

Challenge level

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?
problem
More twisting and turning

Age

11 to 16

Challenge level

It would be nice to have a strategy for disentangling any tangled ropes...
problem
Ace, two, three...

Age

11 to 14

Challenge level

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?