Working systematically

problem
Two egg timers

Age

7 to 11

Challenge level

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
problem
A child is full of ...

Age

7 to 11

Challenge level

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
problem
Number sandwiches

Age

7 to 14

Challenge level

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?
problem
Pair sums

Age

11 to 14

Challenge level

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
problem
Counting factors

Age

11 to 14

Challenge level

Is there an efficient way to work out how many factors a large number has?
problem
W mates

Age

16 to 18

Challenge level

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
problem
Magic W

Age

14 to 16

Challenge level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
problem
Olympic magic

Age

14 to 16

Challenge level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
problem
Plum tree

Age

14 to 18

Challenge level

Label this plum tree graph to make it totally magic!
problem
Magic caterpillars

Age

14 to 18

Challenge level

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.