Wednesday 3 April 2013

mathematics - 1 2 3 4 5 6 7 8 9 = 100


The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For example:


$$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 \times 9 = 100$$


There are possibly hundreds of solutions to this problem, involving different varieties of operators. What is the expression with the fewest number of operators inserted (out of the set $+, -, \times, \div$ and maybe $\sqrt{}$ and $!$) that evaluates to 100?




Answer



I believe that this is the smallest:



$123 - 45 - 67 + 89 = 100$



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