How many isosceles triangles can be constructed so that the : PS Archive
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# How many isosceles triangles can be constructed so that the

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How many isosceles triangles can be constructed so that the [#permalink]

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07 Jul 2006, 07:33
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How many isosceles triangles can be constructed so that the length of each side is a member of the following set?

L={1,2,3,4,5,6,7}

(A) 32 (B) 34 (C) 38 (D) 42 (E) 49
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07 Jul 2006, 09:14
It should be 7P2 minus number of "impossible" combinations, where the sum of 2 sides is less than the 3rd side.

For example, {1,1,3} is impossible triangle. But I counted 12 such impossible combinations, and 42- 12 = 30 is not anong the answers

What did I do wrong?
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07 Jul 2006, 10:02
am getting 30 too.

(1.,1) -- no isosceles triangles possible
(2,2) -- third side can be {1,3} = 2
(3,3) -- {1,2, 4, 5} = 4
(4, 4) -- {1, 2, 3, 5, 6, 7} = 6
(5, 5) = 6
(6, 6) = 6
(7, 7) = 6
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07 Jul 2006, 10:16
Indeed, there are 30 trÂ¡angles. Sorry for any distress! Both methods above are great!
07 Jul 2006, 10:16
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