You are blindfolded before a table. On the table are a very large number of pennies. You are told 128 of the pennies are heads up and the rest are tails up. How can you create two subgroups of pennies, each with the same number of heads facing up, while remaining blindfolded?
Create a subgroup of any 128 pennies. Then flip over all 128. That group of 128 and the group of all the remaining pennies will have the same number of heads facing up.
This works because the "tails" that you grab while making your subset of 128 will equal the "heads" that are left in the original pile. Once you flip your 128 coins over, these "tails" will turn into "heads" and the two groups will have a matching number of heads-up coins.
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Today's brain teaser courtesy of Braingle.com.