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This question already has an answer here:

I was wondering if there are formulas such as min$(a,b)=\displaystyle\frac{a+b-|a-b|}{2}$, etc. but for three numbers (a,b,c).

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marked as duplicate by Eric Towers, fonfonx, Hans Lundmark, Namaste algebra-precalculus Aug 9 '17 at 17:45

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hint

$$\min (a,b,c)=\min (\min (a,b ),c) $$

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    $\begingroup$ I remember that min(a,b,c) ≤ (a+b+c) / 3, which helped me solve the problem. Anyway, thanks for your formula! $\endgroup$ – furfur Aug 9 '17 at 16:08
  • $\begingroup$ Why stop there, Salhamam? $\min(a, b, c) = \min(a,\min(b, c)),$ as well. You never appeal to associativity. $\min(a, b, c) = \min(b, \min(a, c))$, acknowledging the the "minimum operator" is commutative as well as associative. $\endgroup$ – Namaste Aug 9 '17 at 17:51
  • $\begingroup$ @amWhy not salhamam but salahamam. $\endgroup$ – hamam_Abdallah Aug 9 '17 at 18:07
  • $\begingroup$ Oops! Apologies, @Salahamam . The correct spelling is what I intended to write, but I see my fingers and/or my keyboard foiled that intention! :) $\endgroup$ – Namaste Aug 9 '17 at 18:47

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