a chess board has 64 squares if you put 1 pea in the 1st square, 2 in the 2nd, 4 in the 3rd, 8 in the 4th, 16 in the 5th, and continue doubling, up how many peas in the last square.
2006-10-13 11:40:53 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Square 1: 2^0 = 1
Square 2: 2^1 = 2
Square 3: 2^2 = 4
Square 4: 2^3 = 8
...
Square 62: 2^61 = 2,305,843,009,213,693,952
Square 63: 2^62 = 4,611,686,018,427,387,904
Square 64: 2^63 = 9,223,372,036,854,775,808
In words, that is:
nine quintillion, two hundred twenty three quadrillion, three hundred seventy-two trillion, thirty six billion, eight hundred fifty four million, seven hundred seventy-five thousand, eight hundred and eight peas!
That's enough to make a pile at least 30 miles round and 5 miles deep. I don't think your local supermarket carries that many even if you add up the fresh peas, canned peas and the frozen peas.
In reality, there is no way you could fit that many peas on the last square... most of them would roll off, so I'll say there are most likely only 5 or 6 peas still there. :)
2006-10-13 12:05:34 · answer #1 · answered by Puzzling 7 · 1⤊ 0⤋
2^63.
This is because you've got 63 squares filled with powers of 2 and 1 with a 1. So square 2 will be 2, square 3 will be 4, (2^2), square 4 will be 8 (2^3) and so on. Square 64 will be 2^63.
2006-10-13 12:03:52 · answer #2 · answered by Katri-Mills 4 · 0⤊ 0⤋
let's get this absolutely clear
let n= number of squares on the board
the total number of peas required to
cover the whole board= (2^n)-1
the number of peas in the nth
square = 2^(n-1)
the number of peas in the 64th
square = 2^ (64-1) =2^63 a very large number
(9.223372037*10^18 approx)
2006-10-13 19:31:13 · answer #3 · answered by Anonymous · 0⤊ 0⤋
After calculating, I come up with 9223372036854775808 peas on the last square
2006-10-13 11:49:00 · answer #4 · answered by Sassafrass 2 · 0⤊ 0⤋
Given that:
P = number of peas
S = square number
the formula is:
P = 2^(S-1)
P = 2^(64-1) = 2^(63)
P = 9,223,372,036,854,775,808 (i used the calculator for this)
2006-10-13 11:50:36 · answer #5 · answered by naike_10021980 2 · 0⤊ 0⤋
Lots, there is a Chinese fable about a bloke who asked for the emperor to pay him in a similar fashion, one grain of rice on the first square, two on the next and so on, ended up owning a rice mountain
2006-10-13 11:45:36 · answer #6 · answered by Flibble 3 · 0⤊ 0⤋
2^63
A number so large it takes too long to type.
2006-10-13 11:43:28 · answer #7 · answered by Mr Glenn 5 · 0⤊ 0⤋
9223372036854775808
2006-10-13 11:45:43 · answer #8 · answered by Anonymous · 0⤊ 0⤋