This problem will challenge pupils to compare numbers, think ahead and reason logically. They might also be visualising the consequences of moving particular matches, although ideally, there would be real headless matches or lolly sticks available for them to try out their ideas.
In order to encourage children to think logically about this problem rather than just trying random arrangements, you could use the suggested hints
as questions. Pupils could start off by working through the possible arrangements of the 10 matches in a systematic way, for example by beginning with three piles the
same and one different (3, 3, 3, 1 or 2, 2, 2, 4 or 1, 1, 1, 7) then two pairs of piles the same (4, 4, 1, 1 or 3, 3, 2, 2) then two the same and two different (2, 2, 1, 5 or 1, 1, 2, 6 or 1, 1, 3, 5) then all different ... (Finding all these combinations is a challenge in itself.) Chances are that, as they do this, they will begin to realise certain things about whether piles can be the same as
each other or not and what happens if there is a pile of just 1 match. However they discover that consecutive numbers of matches isthe key, there is still more to be investigated if different numbers of matches are used which can then lead to a complete generalisation.