Daily Math Puzzle: 2026-07-18
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2026-07-18
The venerable architects of the ancient city of Kemet designed their grand temples with multiple levels. Each of the 7 levels of the Great Temple of Ra was adorned with exactly 10 sacred frescoes, painted in a single, continuous sequence along its outer wall. While the frescoes on each level were distinct from one another, it was a tradition that the very first fresco on any given level was always an exact copy of the very last fresco of the level directly below it. If an art historian wished to catalog every truly unique sacred fresco in the entire temple, how many unique frescoes would they count from all 7 levels?
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Solution
64 — Initially, one might think there are 7 levels * 10 frescoes/level = 70 frescoes. However, the puzzle states a crucial condition: 'the very first fresco on any given level was always an exact copy of the very last fresco of the level directly below it.'
Let's count:
- The first level has 10 unique frescoes.
- The second level also has 10 frescoes, but its first fresco is a copy of the 10th fresco from the first level. Therefore, only 9 of the frescoes on the second level are truly unique (as the first one has already been cataloged from the level below).
- This pattern repeats for all subsequent levels. For levels 2, 3, 4, 5, 6, and 7, each contributes 9 *new* unique frescoes.
Total unique frescoes = (Frescoes on Level 1) + (New frescoes from Level 2 through Level 7)
Total unique frescoes = 10 + (6 levels * 9 new frescoes/level)
Total unique frescoes = 10 + 54 = 64.
Therefore, an art historian would count 64 truly unique sacred frescoes.
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