Everyday Einstein – 9.2.10

Tomorrow might bring us “tropical storm conditions” according to the NOAA. Well, maybe on the vacation islands along the New England coast. Here’s a puzzle to ponder inside while you keep dry.

From the Mathematical Puzzles of Sam Loyd, selected and edited by Martin Gardner:

“In colonial days, one of the sturdy settlers who had undertaken the difficult task of cultivating the rocky soil off the coast of New England, essayed with the aid of his little daughter Martha, to set out a vineyard. To encourage her, as well as in lieu of other remuneration, he permitted Martha to cultivate for her own use a little square patch containing exactly a sixteenth of an acre of land.

It is said that she planted her vines according to custom, in rows nine feet apart, and cultivated them just like the others, yet, as the story goes, her little venture prospered and grew in a way that made Martha’s Vineyard noted. She raised more grapes to the acre than any vineyard on the island and produced many new and valuable varieties.

That is all there is to the story when it is reduced to plain facts. Nevertheless, without wishing to impeach Martha’s skill nor question her sweetness which imparted the flavor to her grapes, I wish to engraft a practical problem on her vines which may explain the reason for her wonderful success.

How many grape vines, not closer than nine feet apart, can be set out in a square plot one-sixteenth of an acre in size?

Consider that an acre in those parts was 208 feet and 710/1000 of a foot square, so that a sixteenth of an acre is 52 feet 2 inches square.”

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