A question I got from an 8 years old kid:

recreational-mathematics

I got this one from an 8 old kid who got this at school

Can you get the number in the right by using the numbers on the left with the rules:

  1. Each number should be used 1 time exactly,
  2. The allowed operations are: $(,),+,-,\cdot,/$

A solved exercise as an example:

$12$ $11$ $20$ $2$ $= 9$ solution: $(20/2)-(12-11)$

Any ideas regarding the solutions of these three?

$8$ $2$ $1$ $32$ $= 31$

$11$ $2$ $1$ $9$ $= 111$

For example, to me it seems like the first one has no solution.
I can explain it intuitively to myself but I can't prove it formally.
Am I right? If yes, is there a way to formally proof it?

Thanks!

Edit exponentials and roots are not allowed (i.e. $8^2$ is not allowed). All the numbers must be used.
No concatenation is allowed.

Best Answer

I wrote some code to brute-force this instead of doing any hard thinky thinking. Neither {8 2 1 32} = 31 nor {11 2 1 9} = 111 have solutions. If 111 was a typo for 11, $11 + (9+2) \cdot 1$ works.

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