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How many positive three digit even numbers lesser than 700 are there with all three different digits and where the sum of the three digits is 12 or less ?

Am I supposed to write solve the expression for each of the 12 cases like solution for a + b + C=12, 11, 10...1 and then add them together?

Is there a better approach to this problem?

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    I'd start by drawing a tree of cases that begins with the least significant digit, knowing it has to be even. You can then work out the possible choices for upper two digits, taking into account the restriction that all digits are different as well as having sum less than (or equal to??) 12. Note how your title states the last restriction.2011-08-09
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    Less than 12, or 12 or less?2011-08-09
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    @Daniel R Hicks : 12 or less2011-08-09

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