Misprints and Rarities
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#176:The Lake
Sam Loyd (1841-1911) was born in Philadephia (sic) and lived in New York. Loyd was one of the greatest puzzle designers of his time and this is one of his classics:
'I went to Lakewood the other day to attend an auction sale of some land, but did not make any purchases on account of a peculiar problem which developed. The land was advertised as shown in the posters on the fence as 560 acres, including a triangular lake. The three plots show the 560 acres without the lake, but since the lake was included in the sale, I, as well as other would-be purchasers, wished to know whether the lake area was really deducted from the land...the auctioneer guaranteed 560 acres "more or less". This was not satisfactory to the purchasers, so we left him arguing with katydids, and shouting to the bullfrogs in the lake, which in reality was a swamp.
The question which I ask our puzzlists is to determine how many acres there be in that triangular lake, surrounded as shown by square plots of 370, 116 and 74 acres. The problem is of particular interest to those of a mathematical turn, in that it gives a positive and definite answer to a proposition which, according to usual methods, produces one of those ever-decreasing, but never-ending decimal fractions.'
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