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Math questions that don’t make sense in practice, but can nevertheless be solved in theory—for example, a geometry problem contains a triangle whose dimensions make it impossible for it to be constructed.
It’s not uncommon for green authors to set faux math questions, without any suspicion on the part of both teachers and students. Two such examples are the following:

1) Find the perimeter of a triangle with sides 3 cm, 5 cm, and 12 cm.
2) Harry bought a 175-page book. How many digits were used to print the page numbers?

Hints: 1) One can’t form this triangle, because the sum of any two sides must be greater than the third side. 2) The page numbers must be in multiples of 4 or 8.
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by MathPlus April 20, 2018
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