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With gratitude and apologies to the young Gauss . . .

The sum of the first number from each end of the range = 1 + 10,000 = 10,001

The sum of the second number from each end of the range = 2 + 9,999 = 10,001

The sum of the third number from each end of the range = 3 + 9,998 = 10,001

The sum of the fourth number from each end of the range = 4 + 9,997 = 10,001

The sum of the fifth number from each end of the range = 5 + 9,996 = 10,001

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.

etc.

The sum of each pair is 10,001 and there are 5,000 pairs.

The grand total is (5,000) times (10,001) = 50,005,000 .

Q: What is the sum of all numbers 1-10000?

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