Daily Math Puzzle: 2026-08-31
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2026-08-31
In the ancient city of Eldoria, temple records were meticulously carved onto individual stone tablets. The High Scribes used a unique numbering system for sequences of these tablets: the first tablet in any sequence was marked with 1 unique symbol, the next with 2 symbols, the next with 3, and so on, up to a tablet marked with exactly 10 symbols. After a tablet was marked with 10 symbols, the very next tablet would reset and be marked with 1 symbol, repeating the pattern (1, 2, 3, ..., 10). If a newly discovered historical account spans a total of 234 such tablets, how many of these 234 tablets were marked with exactly 7 symbols?
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Solution
23 — The scribes' tablet numbering system follows a repeating pattern: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. This full cycle consists of 10 tablets. Within each complete cycle of 10 tablets, there is exactly one tablet marked with 7 symbols.
First, we determine how many full cycles are contained within the 234 tablets. Divide the total number of tablets by the length of one cycle:
234 tablets / 10 tablets per cycle = 23 full cycles with a remainder of 4 tablets.
Each of the 23 full cycles contains exactly one tablet marked with 7 symbols. So, from the full cycles, we have 23 tablets marked with 7 symbols.
Next, we examine the remainder of 4 tablets. These remaining tablets would be marked sequentially starting from 1 again: 1, 2, 3, 4. None of these remaining 4 tablets are marked with 7 symbols, as the highest symbol count in this remainder sequence is 4.
Therefore, the total number of tablets marked with exactly 7 symbols is 23 (from the full cycles) + 0 (from the remainder) = 23 tablets.
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