I am interested in puzzles and games and how they relate to mathematical thinking, not least through my involvement with the Maths Arcade initiative. I was pleased to read what is said on this topic in the 1982 Cockcroft report. This is the report of an inquiry started in 1978 “to consider the teaching of mathematics in primary and secondary schools in England and Wales, with particular regard to its effectiveness and intelligibility and to the match between the mathematical curriculum and the skills required in further education, employment and adult life generally”.

On puzzles and games, the report says:

The inherent interest of mathematics and the appeal which it can have for many children and adults provide yet another reason for teaching mathematics in schools. The fact that ‘puzzle corners’ of various kinds appear in so many papers and periodicals testifies to the fact that the appeal of relatively elementary problems and puzzles is widespread; attempts to solve them can both provide enjoyment and also, in many cases, lead to increased mathematical understanding. For some people, too, the appeal of mathematics can be even greater and more intense.
…
We do not believe that mathematical activity in schools is to be judged worthwhile only in so far as it has clear practical usefulness. The widespread appeal of mathematical puzzles and problems to which we have already referred shows that the capacity for appreciating mathematics for its own sake is present in many people. It follows that mathematics should be presented as a subject both to use and to enjoy.
…
Whatever the level of attainment of pupils, carefully planned use of mathematical puzzles and ‘games’ can clarify the ideas in a syllabus and assist the development of logical thinking.

Cockcroft, W. (1982), Mathematics counts: report of the Committee of
Inquiry into the teaching of mathematics in schools. London: HMSO.