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Integers from 1 to 10000 are written orderly in a grid of 100×100, as shown in the table below.

What is the sum of the numbers in the two diagonals highlighted in yellow?

 

 Jul 17, 2020
 #1
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Each of the diagonals is an arithmetic series.

 

The formula for the sum of an arithmetic series is:  Sum  =  n(a1 + an) / 2

where         n = number of terms         a1 = first term         an = last term

 

For the diagonal from upper left to lower right:  n = 100     a1 = 1     an = 10000

--->     Sum  =  100( 1 + 10000 ) / 2  =  500 050

 

For the diagonal from upper right to lower left:  n = 100     a1 = 100     an = 9901

--->     Sum  =  100( 100 + 9901 ) / 2  =  500 050

 

You'll need to add these two sums together to get the final answer ...

 Jul 18, 2020

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