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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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Solution By hand | Comment 4 of 7 |
5 always has to be one of the numbers, so this is equivalent to looking for two numbers less than 9 whose product is divisible by 4.  I did it by hand, and seem to have found 21 (same as Ed).  I found it easier to order decreasing.  My list

98, 96, 94

88, 87, 86, 85, 84, 83, 82, 81

74

66, 64, 62

54

44, 43, 42, 41

22

 

  Posted by Steve Herman on 2010-03-31 14:18:25
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