The numbers 1, 2, 3, ..., 2007, 2008 are recorded on a sheet of paper. You may cross out any two numbers and replace them by their difference. If you repeat this operation enough times, a single number will be left. Is this number even or odd? Why?

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- Nov 18th 2008, 05:55 AM #1

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## Even or Odd

The numbers 1, 2, 3, ..., 2007, 2008 are recorded on a sheet of paper. You may cross out any two numbers and replace them by their difference. If you repeat this operation enough times, a single number will be left. Is this number even or odd? Why?

- Nov 18th 2008, 06:07 AM #2

- Nov 18th 2008, 12:05 PM #3