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You don't need advanced algebra to prove that it is impossible to trisect a line segment using only a straight edge and a compass: anyone knows that you will also need a pencil! And one you have that then there are plenty of easy ways to do it.
Inifinitely many ways, for example: 101 - 1, 102 - 2, 103 - 3, etc. Note that in each case, no number was used more than once.
you can make 40 cents withiut using pennies 7 ways
6 ways.6 ways.6 ways.6 ways.
24 ways