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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.

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (2 votes)

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Solution yes, they do Comment 2 of 2 |

1.  Out of any 4 numbers at least two are equal modulo 3

2.   The following table presents the quantity of even differences

for any number of even numbers in the chosen set of four:

0  EVEN NUMBERS...............6  EVEN differences

1........................................3

2........................................2

3 .......................................3

4..........................................6

this .shows that the PRODUCT will include factors 3 and 2^2

i.e. will be a multiple of 12.

 


  Posted by Ady TZIDON on 2007-03-28 07:39:50
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