## le compte est bon

**T**he Riddler asks how to derive 24 from (1,2,3,8), with each number appearing once and all operations (x,+,/,-,^) allowed. This reminded me of a very old TV show on French TV, called Le compte est bon!, where players were given 5 or 6 numbers and supposed to find a given total within 60 ,seconds. Unsurprisingly there is an online solver for this game, as shown above, e.g., 24=(8+3+1)x2. But it proves unable to solve the puzzle when the input is 24 and (2,3,3,4), only using 2,3 and 4, since 24=2x3x4. Introducing powers as well, since exponentiation is allowed, leads to two solutions, (4-2)³x3=(4/2)³x3=(3²-3)x4=3/(2/4)³=24… Not fun!

I however rewrote an R code to check whether 24 was indeed a possibility allowed with such combinations but could not find an easy way to identify which combination was used, although a pedestrian version eventually worked! And exhibited the slightly less predictable 4^{3/2}x3=24!

July 22, 2020 at 8:11 am

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