2006 SMT/General Problems/Problem 13

Problem 13

$123456789=100$ . Here is the only way to insert $7$ pluses and/or minus signs between the digits on the left side to make the equation correct: $1+2+3-4+5+6+78+9=100$ . Do this with only three plus or minus signs.

Solution

This solution does require quite a bit of guessing and testing, but if we notice that we want the numbers to be relatively close so that no term "dominates" the sum, we see that the solution is $\boxed{123-45-67+89=100}$

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2006 SMT/General Problems/Problem 13

Problem 13

Solution