Imagine a chess board. Put a wheat grain in the first square, then two on the next. Double the amount of grains on each of the following squares. (example: 1, 2, 4, 8, 16...) How many wheat grains will you have in total when you finish filling the 36 squares whith the double amount of grains that you have in the prior square? (in total, how many grains will you have on the board?)
2006-09-25 11:33:25 · 9 answers · asked by Mardesal 2 in Science & Mathematics ➔ Mathematics
No genius required. That is a summation equation related to exponential growth. Also, there are 64 squares on a chess board. This sounds like a homework problem. Just be sure to get the correct number of squares.
2006-09-25 11:40:59 · answer #1 · answered by Jack 7 · 0⤊ 0⤋
Chess boards have 64 squares, not 36. For a board with 64 squares there would be a total of 2^64-1 grains.
2^64 - 1 = 18,446,744,073,709,551,615
2006-09-25 11:39:44 · answer #2 · answered by professional student 4 · 0⤊ 0⤋
using geometric proggressions we solve the sum
a(first no.)=1
common ratio(increase in no. of grains)=2
n(last no)or(no. of squares)=36
sum=a[r^n-1]/r-1
=1[2^36-1]/35
=68719476739/35=1963413621
last no=64
sum=1[2^64-1]/63
=[{1844674407*10^10}-1]/63
=2928054614*10^8
answers:
1)total no. of wheat grains in 36 squares=1963413621grains
2)total no. of weat grains in all squares=2928054614*10^8grains
2006-09-25 21:20:43 · answer #3 · answered by Anonymous · 0⤊ 0⤋
That's pretty funny. There are 64 squares on a chessboard.
The answer (with a 64-square chessboard) would be
2^64 - 1
which is
18446744073709551615
2006-09-25 11:37:46 · answer #4 · answered by Anonymous · 1⤊ 0⤋
36 squares: 2^36-1
in total: 2^64-1
2006-09-25 11:37:03 · answer #5 · answered by need help! 3 · 1⤊ 0⤋
68,719,476,735 is the total for 36 squares, not 34,359,738,367 which would be the total for 35 squares.
2006-09-25 11:51:33 · answer #6 · answered by Wren 3 · 0⤊ 0⤋
18,446,744,073,709,551,615
damn, too slow
But 36 squares would be:
34,359,738,367
2006-09-25 11:40:01 · answer #7 · answered by Anonymous · 0⤊ 0⤋
There are 64 squares on a chess board.
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
rook, knight, bishop, queen, king, bishop, knight, rook
It would be (2^64) - 1
2006-09-25 11:43:07 · answer #8 · answered by Anonymous · 1⤊ 0⤋
122,138,120
2006-09-25 11:51:58 · answer #9 · answered by Anonymous · 0⤊ 0⤋