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Concerning combinatorics (Posted on 2011-10-04) Difficulty: 3 of 5
Take a row of Pascals Triangle. Write a second copy of the row below it but with an offset. Multiply each pair of numbers and then sum these products. (A missing number is considered to be zero.)

The result is number further down the Triangle.

Can you explain or prove the result?

Example with the 4th row and offset by 1:

1    4    6    4    1    0
0    1    4    6    4    1
0 +  4 + 24 + 24 +  4 +  0 = 56 which is in row 8.

No Solution Yet Submitted by Jer    
Rating: 4.5000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some Thoughtsre: 1 step further. Not commutative.Bractals2011-10-07 07:30:00
1 step furtherSteve Herman2011-10-06 00:45:18
Some Thoughts1 step further.Jer2011-10-05 10:53:14
Hints/Tipsre: Happy 35th anniversary (spoiler) -my wayAdy TZIDON2011-10-05 10:01:33
SolutionHappy 35th anniversary (spoiler)Steve Herman2011-10-04 23:55:12
Result explaned - No ProofBractals2011-10-04 12:56:56
Some ThoughtsPossible explanationbroll2011-10-04 12:53:20
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