Question 69099
Well, you can start by noting that the number of grains of wheat, starting with one on the firsy square, double for each succeeding square.  This can be represented by powers of 2 as shown below.  If we let n be the number of the square (for the first square, n=1, for the second square, n=2, etc) you can make a table showing the progression of the number of grains on the squares.
n...# of grains
--------------
1.....1
2.....2
3.....4
4.....8
5.....16
It doesn't take long to see that this can be represented by the following"
n. .... grains
--------------
n=1...{{{1=2^0}}}
n=2...{{{2=2^1}}}
n=3...{{{4=2^2}}}
n=4...{{{8=2^3}}}
n=5...{{{16=2^4}}}
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For the nth square only, the number of grains is {{{2^(n-1)}}}

The number of grains on the 24th square only, would be {{{2^(24-1) = 2^23}}} = 8,388,608
The total number of grains on the board is given by:
({{{1+2^1+2^2+2^3}}}...{{{2^n}}}) - 1
Now if the checker board had only 24 squares and each square is filled according to the above scheme, then the total number of grains is:
{{{2^24-1 = 16777215}}}

To fill the entire board of 64 squares, you would need:
{{{2^64-1}}} = 18,446,744,073,709,551,615 grains of wheat.