Get your checkerboard and place one grain of wheat on the first square. Then place two grains of wheat on the next square. Then place four grains on the third square. Continue this until all 64 squares are covered with grains of wheat.” As he had just harvested his wheat, Mr. Crane did not consider this much of an award, but he soon realized he made a miscalculation on the amount of wheat involved.
How much total grain would the traveling salesman receive if the checkerboard only had 24 squares?
Calculate the amount of wheat necessary to fill the whole checkerboard (64 squares). How much wheat would the farmer need to give the salesman? Please provide the answer in either scientific notation, or calculate and show all 20 digits.
2007-07-04 15:51:40 · 5 answers · asked by quepid622 1 in Science & Mathematics ➔ Mathematics
yeah what that last guy said
2007-07-04 15:58:49 · answer #1 · answered by Takumi 3 · 0⤊ 0⤋
square N 2^N
1 0 1
2 1 2
3 2 4
4 3 8
5 4 16
6 5 32
7 6 64
8 7 128
9 8 256
10 9 512
11 10 1024
12 11 2048
13 12 4096
14 13 8192
15 14 16384
16 15 32768
17 16 65536
18 17 131072
19 18 262144
20 19 524288
21 20 1048576
22 21 2097152
23 22 4194304
24 23 8388608
total 16777215
Total for the checkerboard:
9223372036854780000
2007-07-04 23:03:20 · answer #2 · answered by telsaar 4 · 0⤊ 0⤋
This is a geometric sequence.
Your common ratio is 2 and your beginning term is 1.
Total # of Grains = (1 - 2^64) / -1 or (2^64 -1)
For 24 squares it would be:
(2^24-1)
Find your own answer with a calculator.
Formula for sum of a geometric sequence.
b1 * ( 1-r^n) / (1-r)
b1 = first term
n= the nth term
r = common ratio
2007-07-04 22:59:03 · answer #3 · answered by UnknownD 6 · 0⤊ 0⤋
2^24 - 1 = 16,777,215 grains
2^64 - 1 = 18,446,744,073,709,551,615 grains
2007-07-04 23:01:13 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
24 squares: total 2²⁴-1=16,777,215
64 squares: 2⁶⁴-1=18,446,744,073,709,551,615
2007-07-04 22:56:45 · answer #5 · answered by yupchagee 7 · 0⤊ 0⤋