Working systematically

Alberta won't reveal her age. Can you work it out from these clues?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?

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

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

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

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

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

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?

Can you make the numbers around each face of this solid add up to the same total?

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