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Differences Do Dozen? (Posted on 2007-03-28) Difficulty: 2 of 5
Pick four integers. Calculate their six pairwise differences. Multiply all those differences. Prove that the result is a multiple of 12.

  Submitted by Old Original Oskar!    
Rating: 4.0000 (2 votes)
Solution: (Hide)
If there are two odd and two even numbers, two of the differences will be even, and thus the product will be a multiple of four. If there are three or four numbers of the same parity, then three or more of the differences will be even.

Out of the four numbers, two must be congruent mod 3, so their difference is a multiple of three.

Both results together imply the answer to this puzzle.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionyes, they doAdy TZIDON2007-03-28 07:39:50
SolutionDozenJer2007-03-28 07:33:45
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