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In 100 numbers you can select 50 all odd or 50 all even and there will be no consecutive pair. Picking another number must be of the opposite parity and so consecutive with one of your first 50.

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Q: Show that if we select 51 distinct numbers from 1 to 100 at least two are consecutive numbers.?
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The sum of 3 consecutive numbers is 600 what is the least of these 3 numbers?

The least of the three numbers is 199.

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