Daily Math Puzzle: 2026-06-09
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2026-06-09
Archaeologists uncovered a series of stone tablets from the lost civilization of Xal'kara. Each tablet bears a single digit that follows a simple rule: the number 1 appears once, the number 2 appears twice, the number 3 appears three times, the number 4 appears four times, and so on. The sequence of digits on the tablets therefore reads: 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, … If a researcher picks up the 15th tablet in this order, what digit will be on it?
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Solution
5 — The pattern is that the integer n appears exactly n times. The total number of tablets up to and including the block of n’s is the triangular number Tₙ = n(n+1)/2. We need the smallest n such that Tₙ ≥ 15. For n=5, T₅ = 5·6/2 = 15, so the 15th tablet is the last one in the block of five 5’s. Therefore the digit on the 15th tablet is 5, which corresponds to choice index 2.
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