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Counting triplets (Posted on 2010-03-31) Difficulty: 3 of 5
For how many ordered triplets (a, b, c) of positive integers, each less than 10 is the product abc divisible by 20?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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re: Solution (interpretations) | Comment 3 of 7 |
(In reply to Solution (interpretations) by ed bottemiller)

Ordered in math means the order is important.  The ordered pair (5,4) is not the same point as (4,5) on the Cartesian plane.

Polar coordinates are not ordered as long as units are specified since (5,30degrees) and (30degrees, 5) are the same even though the former is conventional.

Assuming your 20 nondescending triplets, 14 strictly ascending is accurate.

14*6 permutations + 6*3 permutations = 102 ordered triplets.

  Posted by Jer on 2010-03-31 14:09:23

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