Daily Math Puzzle: 2026-04-10
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2026-04-10
The kingdom of Eldoria is assembling a quest party of exactly five members. The party can only be made up of elves, dwarves, and humans, and there must be at least one of each race. How many different possible race‑composition combinations can the party have?
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Solution
6 — Let e, d, h be the numbers of elves, dwarves, and humans. We need e + d + h = 5 with each ≥ 1. Subtract 1 from each variable to satisfy the minimum: (e‑1) + (d‑1) + (h‑1) = 2, where the new variables are non‑negative. The number of non‑negative integer solutions to x + y + z = 2 is given by the stars‑and‑bars formula C(2 + 3 – 1, 3 – 1) = C(4, 2) = 6. Therefore there are 6 distinct race‑composition possibilities.
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