Working systematically

problem
Button-up

Age

5 to 7

Challenge level

My coat has three buttons. How many ways can you find to do up all the buttons?
problem
Difference dynamics

Age

14 to 18

Challenge level

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
problem
Same number!

Age

14 to 16

Challenge level

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?
problem
Sociable cards

Age

11 to 14

Challenge level

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?
problem
Curious number

Age

7 to 11

Challenge level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
problem
The square of my age

Age

11 to 14

Challenge level

Lauren and Thomas tell their ages in terms of sums of squares. Can you work out how old they really are?
problem
Rolling along the trail

Age

11 to 14

Challenge level

What could be the scores from five throws of this dice?
problem
Double with 1 to 9

Age

11 to 14

Challenge level

Can you find a number and its double using the digits $1$ to $9$ only once each?
problem
Alberta's age

Age

14 to 16

Challenge level

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

Age

11 to 14

Challenge level

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