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St. Ives problem





A well-known and simple puzzle in arithmetic set by Mother Goose in the rhyme "As I Was Going to St. Ives":
As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, and every sack had seven cats, every cat had seven kittens. Kittens, cats, sacks, and wives, how many were going to St. Ives?
The various individuals and items make up a geometric series: 7 wives + 72 sacks + 73 cats + 74 kittens = 7 + 49 + 343 + 2401. This gives a total of 2800 (or 2801 if the narrator also happens to be a wife). A similar problem, and solution, is contained in the Rhind papyrus by Ahmose, written about 1650 BC (some of which is copied from an older document of about 1800 BC). Here the geometric series has one more power of 7: 7 houses + 49 cats + 343 mice + 2,401 ears of grain + 16,807 hekats (a measure) of grains, giving a total of 19,607.


Related categories

   • GAMES AND PUZZLES
   • ARITHMETIC