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Operator Searches

Solve problems in reverse using the rules of arithmetic!

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Operator searches are puzzles for equations that can be solved with a mix of logic, creativity, and number theory.

Of course \(8 + 8 + 8 + 8 = 32,\) but what operators can you use to make the equation below true?

\[8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ 8 \ \ \ = \ \ \ 32\]

Here are some of the solutions that we've come up with. Can you find any others? \[\begin{align*} (8 + 8)\times (8 + 8) \div 8 &= 32 \\ (8\times8\times8) รท (8 + 8)&= 32 \\ 8- 8 \div 8 - 8 \div 8 &=3 \times 2 \end{align*}\]

Here is one last example to get your mind racing! Using any operators (and parentheses if needed), can you make this true? Get creative!

\[1\, \square\, 1\, \square\, 1\, \square\, 1\, = 5\]

Master the problem solving skills of Joy of Problem Solving.

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