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Eight queens — Trial, pattern and proof

Ages 9 and up · about 8 minutes · 8by8verse Chess Lab

What it teaches

Working systematically, spotting symmetry, and reasoning about what is impossible.

The story to tell first

In 1848 a chess player named Max Bezzel asked a question in a magazine: can eight queens stand on a chessboard so that none attacks another? Mathematicians could not leave it alone. There turned out to be exactly 92 ways.

Three questions to ask

• Why can no two queens share a row? What does that tell you about where to start?
• Turn your answer a quarter turn. Is it a new answer or the same one?
• Why is there no answer at all on a three-by-three board?

Without a screen

Use eight counters on a paper board. Pairs race to find one answer, then compare — are any two the same answer turned around?