I got this puzzle from a book, I think, but I would be hard-pressed to remember which one. In any case, I believe that it is relatively well-known. Although quite simple, I feel that it has a pleasing air of algebraic mystery about it. I have also found that it is a particularly good question for A-level students to check their understanding of algebra, along with their general problem-solving skills.
Difficulty: *
Maths knowledge required: GCSE algebra [i.e. 14-16 year olds]. Although KS3 would do….
Puzzle:
Simplify this expression:
(x − a) (x − b) (x − c) … (x − z)
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Click HERE for the solution.
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DIFFICULTY RATINGS:
* – Not too taxing
** – Requires significant thought
*** – Extremely difficult
!!!! – Requires high level mathematics / Unsolved / Insoluble
Thomas Oléron Evans, 2015