Working systematically

problem
No square sums

Age

14 to 16

Challenge level

How many numbers do you need to remove to avoid making a perfect square?
problem
Kangaroo hops

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

This grocer wants to arrange his fruit in a particular order, can you help him?
problem
Factor list

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

The squares of this grid contain one of the letters P, Q, R and S. Can you complete this square so that touching squares do not contain the same letter? How many possibilities are there?
problem
Facial sums

Age

14 to 16

Challenge level

Can you make the numbers around each face of this solid add up to the same total?
problem
Grid without lines

Age

11 to 14

Challenge level

Can you remove the least number of points from this diagram, so no three of the remaining points are in a straight line?
problem
AP train

Age

16 to 18

Challenge level

An arithmetic progression is shifted and shortened, but its sum remains the same...
problem
Trig identity

Age

16 to 18

Challenge level

In this short challenge, can you use angle properties in a circle to figure out some trig identities?