as we all know there r 64 cheks on a chessboard
if in the first box 1 grain is kept
in 2nd box 2 grains,
in the next if u keep 4 grains
and so on
how many will u keep in 64th box
2006-10-07 03:08:33 · 34 answers · asked by sahi 2 in Science & Mathematics ➔ Mathematics
First square - 2^0 = 1
Second suare - 2^1 = 2
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nth square - 2^(n-1)
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64th square 2^63 - a very very large no. Much more that total no. of grains in the world!!!!!!!!!!!!!!
2006-10-07 06:32:13 · answer #1 · answered by Teepy 2 · 1⤊ 1⤋
In the 64th box you can keep 2 raised to the power 63 grains
2006-10-07 03:27:24 · answer #2 · answered by ajit k 1 · 3⤊ 1⤋
By using the formulae: tn = a x r to the power (n-1)
Where, tn = no. of grains in the 64th box, a = no. of grain in the first box i. e. 1, r = common ratio (as the no. of grains to be doubled in successive box, it is twice as much as in the preceeding box hence 2), n = no. of terms (in this case it is 64)
This way the number of grains in the 64th box will be
1 x 2 to the power 63.
2006-10-07 03:20:23 · answer #3 · answered by Gorkhali Kanchha 2 · 3⤊ 1⤋
yep
the formula is
2^(b-1) where b is the box number. (2 raised to the power of b-1)
so 2^3 = 8 is what is in the 4th box..
substatute 64 for b for the answer
its 2^63
2006-10-11 23:28:25 · answer #4 · answered by Nick 3 · 0⤊ 0⤋
Have used excel commands and this is the answer : 9223372036854780000
To calculate according to GP the series would be
1,2, 4, 8, 16, 32, 64 ,.............
Last term = ar^(n-1)
a = 1, r = 2, n= 64 (no of boxes = 64)
This implies last term is = 2^63 which should be equal to 9223372036854780000
Joint venture by self and my dearest daughter
For confirmation use excel sheet. write the formulas and get values for first row. then copy paste for 64 rows.
2006-10-07 23:55:41 · answer #5 · answered by PG 2 · 0⤊ 1⤋
First box 1, 2nd box 1 x 2, 3rd Box 1x2x2, 4th box 1x2x2x2 (get the pattern?
Any box number has grains = 2 to the power box number.
So in the 64th square you will have 2 to the power 64.
=1.84467E+19
2006-10-07 03:24:54 · answer #6 · answered by Anonymous · 0⤊ 3⤋
2^63 grains in the 64th box
2006-10-07 03:20:36 · answer #7 · answered by sarvani_nadi 1 · 1⤊ 1⤋
2^63 grains in the 64th box
2006-10-07 03:56:31 · answer #8 · answered by smiley 1 · 2⤊ 1⤋
2 to the power of 63
2006-10-12 18:05:40 · answer #9 · answered by Balajee 1 · 0⤊ 0⤋
1st box = (2)0 = 1
2nd box = (2)1 = 2
3rd Box = (2)2 = 4
4th box = (2)3 = 8
etc...
64th box = (2)63 = 9223372036854775808
2006-10-07 17:13:55 · answer #10 · answered by django_of_djangos 1 · 1⤊ 1⤋
You can infer that it is in geomatric progression.
Therefore we have to calculate 'n'th term which is given as
n term = ar^n-1
Here a=1 & r=2
n term =1*2^64-1
n term=2^63 is the answer
Therfare i would fill 2^63 grains
2006-10-07 07:44:32 · answer #11 · answered by Pawan 1 · 1⤊ 1⤋