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Quandaries & Queries
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 Topic: powers of 2
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 A cylinder is to be filled with peas. 2012-06-12 From Silje:Hi! How can I solve the following question without the use of a calculator? "A cylinder is to be filled with peas. It is done like this: At 12:00 o'clock you put 1 pea in, at 12:01 you put 2 peas in, at 12:02 you put 4 peas in, at 12:03 you put 8 peas in, and so on. This continues until 14:00 o'clock (two hours later), when the last peas are put in and the cylinder is full. At what time is the cylinder half full?"Answered by Robert Dawson. Collecting an army 2009-02-25 From bevaz:Question from bevaz, a student: A ruler orders his chamberlain to collect an army from 30 houses. The servant goes to the first house alone and collects one man. At each house after that he takes the same number of men as he has already collected, so at the second house he goes with one other and so on. How many men did he collect in all?Answered by Penny Nom. The nth term of a sequence 2008-09-13 From lavett:what is the Nth term in the sequence when the sequence is 2,4,8,16... and the term numbers are 1,2,3,4...Answered by Stephen La Rocque. Does the sequence 1 2 4 8 16 32 etc have a name? 2008-07-17 From Richard:Just an idle thought really. Does the simple sequence 1 2 4 8 16 32 etc have a name?Answered by Victoria West. 1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 2008-01-22 From Neil:Find the next two terms in the following number sequence 1/2, 1/2, 3/8, 1/4, 5/32, 3/32, 7/128 Find a general rule for the nth term of the sequenceAnswered by Penny Nom. The number of decimal places in 1 over a power of 2 2002-09-12 From Allan:Does anyone notice that the maximum number of decimal place of the number 2 dividing 1 and its increment (4, 8, 16...etc) is the same as the power of number 2? eg. 22=4, thus the max number of decimal of 1/4=0.25 which is 2 decimal place and 2 is the number of power of 2 take 64 as example: 26=64, and take 1/64=0.015625 which has 6 decimal place (and is the power 6) Is there such a law in math? If yes, can you tell me what it is? Or is this my discovery? Answered by Paul Betts.

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