Rhind Mathematical Papyrus
A similar problem is found in the Rhind Mathematical Papyrus (Problem 79), dated to around 1650 BC. The papyrus is translated as follows:
| houses | 7 | |||
| 1 | 2,801 | cats | 49 | |
| 2 | 5,602 | mice | 343 | |
| 4 | 11,204 | spelt | 2,301 | |
| hekat | 16,807 | |||
| Total | 19,607 | Total | 19,607 |
The problem appears to be an illustration of an algorithm for multiplying numbers. The sequence 7, 7 × 7, 7 × 7 × 7, ..., appears in the right-hand column, and the terms 2,801, 2 × 2,801, 4 × 2,801 appear in the left; the sum on the left is 7 × 2,801 = 19,607, the same as the sum of the terms on the right. Note that the author of the papyrus miscalculated the fourth power of 7; it should be 2,401, not 2,301. However, the sum of the powers (19,607) is correct.
The problem has been paraphrased by modern commentators as a story problem involving houses, cats, mice, and grain, although in the Rhind Mathematical Papyrus there is no discussion beyond the bare outline stated above. The hekat was 1⁄30 of a cubic cubit (approximately 4.8 l, 1.1 imp gal; 1.3 US gal).
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