# Puzzle-metapuzzle pairs

When I was at school, I thought that a good puzzle should have a solution. In my first year at college I encountered the idea of a "solution set". This was mind-expanding. A puzzle has a set of solutions: often it has one member, but it may have none, or many.

When I was at college, I came across puzzles like this:

` If dim`_{F} v = *n* prove that dim_{F} (Hom(V,V)) = *n*^{2}.

I realised that the setter will have been thinking "the pupil will know what all this stuff means. The challenge is to find a proof." In reality, the pupil might not know what dim_{F} means. The challenge is to come up with a plausible meaning for dim_{F} such that the proof is possible but not trivial.

I regard such puzzles as metapuzzle/puzzle pairs. The metapuzzle is to come up with a plausible interpretation of the puzzle statement; the puzzle is to solve that interpretation. If the puzzle is too easy or too hard, maybe you've got the metapuzzle wrong.

I once regarded such metapuzzle/puzzle pairs as a defective puzzles, which had accidentally acquired a metapuzzle wrapping. Now, I regard any puzzle statement as a metapuzzle/puzzle pair. Sometimes the metapuzzle is trivial, but I don't know that until I've solved the puzzle, or at least convinced myself that it may well have an interesting solution. This viewpoint doesn't just apply to abstract algebra puzzles like the one above, but also to some old chestnuts like "what colour is the bear", "manhole covers", and "Monty Hall" in the list below.

## Some examples

What colour is the bear?

Bolleke puzzle on beermat

Simultaneous equations

Four colliding ships

Manhole covers

The Monty Hall puzzle

Six points on a disk

Numbers in a car park

Ants and triangle

Two points on the equator

A sliding block puzzle

Doppler effect question

Square question

Square square pyramidal number

Tornado question

This is one of several miscellaneous pages listed at http://www.weddslist.com/writing/.