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A children's fairy tale tells of a clever elf who extracted from a king the promise...

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Advance Math

A children's fairy tale tells of a clever elf who extracted froma king the promise to give him one grain of wheat on a chess boardsquare today, two grains on an adjacent square tomorrow, fourgrains on an adjacent square the next day (and so on), doubling thenumber of grains each day until all 64 squares on the chess boardwere used.

(a) How many grains of wheat did the hapless king contract toplace on the 64th square?


(b) There are about 1.1 million grains of wheat in a bushel. Assumethat a bushel of wheat sells for $4.40. What was the value of thewheat on the 64th square?

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