Maths Olympiad Prep

Track / Stage 5 / 32 of 400 #632 of 1964

Problem 632

AIME late
Combinatorics Difficulty 5.1 Find the answer

The Constellation Puzzle. The group of stars depicted in the figure is very difficult to spot even on the clearest night for the simple reason that it... is invisible. 21 stars of this constellation form 7 straight lines with 5 stars on each.

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Could you rearrange the stars so that they form 11 straight lines with 5 stars on each? There are many solutions to this puzzle. Try to find a symmetrical one.

The source for this one didn't record the answer, so there is nothing to check what you type against. Work it on paper and mark yourself against the solution below.

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Official solution

430. The figure shows a symmetrical solution in which 21 stars form 11 lines with 5 stars on each line.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.