Stranger Math

Algebra Level 3

In the year 4231, an astronaut travels to a planet with intelligent life. The astronaut saw numerous math equations written in the planet, and deduced that they were using a different set of notation. He saw the following arithmetic equations:

\(6\times 8=24\)
\( 20\times 12=60\)
\( 60\times 24=120\)
\(52\div 42=2\)
\(69\div 24=3\)
\(202\div 101=101\)
\(\left| 32 \right| =6\)
\(\left| 55 \right| =\left| 10 \right| =1\)
\(\left| 82+3 \right| =\left| 10+3 \right| =\left| 1+3 \right| =4\)
\(\left| 36-23 \right| =\left| 9-5 \right| =4\)
\(\left| 6\times 8 \right| =24\)
\( \left| 20\times 12 \right| =60\)
\(\left| 52\div 42 \right| =2\)
\(\left| 69\div 24 \right| =3\)

In order for him to gain an audience with the ruler, he needs to solve this equation using these same rules:

\[ \left| 32\div \left\{ 36-\left[ 58+\left( 32\times 3 \right) \right] \times \left[ 45+\left( 36-2 \right) \right] \right\} \right|. \]

Help him to solve this strange problem.

Hint: To find logic in these equations, you can use LCM, GCD, and the sum of the digits of these numbers.
The order of operations is the same on this planet and on Earth: First the parentheses, after the brackets, braces, multiplication, division, etc.


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