Daily Math Puzzle: 2026-05-18
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2026-05-18
Eight teams are placed at equal intervals around a circular track, which forms the vertices of a regular octagon. Every pair of teams must play exactly one match, and each match is played on a straight line connecting the two teams’ positions. A "shortcut" match is defined as a match whose line is either a side of the octagon or the shortest possible diagonal (i.e., it skips exactly one vertex). How many shortcut matches are played in total?
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Solution
16 — The eight teams sit at the vertices of a regular octagon. A shortcut match can be:
1. A side of the octagon. There are 8 sides.
2. The shortest diagonal, which connects a vertex to the one two steps away (skipping exactly one vertex). Each vertex has 2 such diagonals, but each diagonal is shared by two vertices, so the total number of these diagonals is (8 × 2) ÷ 2 = 8.
Adding them together gives 8 + 8 = 16 shortcut matches. Therefore, the correct answer is 16, which is choice index 1.
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