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How many three-digit numbers are composed of three distinct digits suc

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How many three-digit numbers are composed of three distinct digits suc  [#permalink]

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New post 14 Mar 2019, 03:11
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Difficulty:

  75% (hard)

Question Stats:

27% (01:52) correct 73% (03:00) wrong based on 22 sessions

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Re: How many three-digit numbers are composed of three distinct digits suc  [#permalink]

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New post 17 Mar 2019, 20:53
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Pick 3 single digit numbers such that the gap between them are the same, which can be 1, 2, 3, or 4. That way, the middle will be the average of the other two. Remember to subtract the numbers that begin with 0 since we want three digit numbers.

0,1,2; 1,2,3 ... 7,8,9 = 8 groups
0,2,4; ... 5,7,9 = 6 groups
0,3,6; ... 3,6,9 = 4 groups
0,4,8; 1,5,9 = 2 groups

So 20 different groupings of numbers, each with 3! ways to arrange them or 120. Subtract the 8 numbers that began with 0 since those are two digit numbers, and you get 112

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Re: How many three-digit numbers are composed of three distinct digits suc   [#permalink] 17 Mar 2019, 20:53
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