## St. Ives

This famous rhyme is apparently from Mother Goose:

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?

It is seldom mentioned that, since the narrator is going to St. Ives, these other charming folks (and their possessions) are obviously coming from St. Ives, not going to St. Ives. So, the narrator is the only one going to St. Ives. The puzzle specifies kittens, cats, sacks, and wives. The narrator may or may not be a wife. So, the answer is either zero or one.

Aside from that, there are 7 wives (maybe 8 if the narrator is a wife), 49 sacks, 343 cats, and 2401 kittens (a geometric series). The total is 2800 (maybe 2801 if the narrator is a wife).

There is a very similar puzzle in the Rhind Mathematical Papyrus by Ahmose, written about 1650 BCE (some of which is copied from an older document of about 1800 BCE). Actually it is not stated as a puzzle, but as a solution:

 7 houses 49 cats 343 mice 2301 (typo) ears of grain 16807 hekat of grain 19607

2301 should be 2401. A hekat is a measure of grain. There is one more power of seven here, than in the Mother Goose version.

The Egyptian text also shows that the total (19,607) is 7x2801. 2800 is the sum of the first four terms of the series. The problem is perhaps given to show that the sum of the geometric series S(n), which starts with r (the common ratio, 7 in this case) is r(S(n-1)+1), where S(n-1) is the previous sum.