# Without trial and error, average(average(a,b),c) vs. average(a,average(b,c)). [closed]

**Closed**
as unclear
by Peter Taylorâ€
on Nov 27, 2021 at 20:54

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EXCLUDE Trial and Error. If $a = b = c = 0$, then obviously both sides are equal. My child is 14 y.o. We prefer pretty proofs by picture (but beware), AND intuition! Recondite algebra is not required.

But how do I systematically deduce when $\overline{\overline{a, b}, c} = \frac{a}{4}+ \frac{b}{4} + \frac{c}{2}$

- = AND
- $\neq$

$\overline{a, \overline{b, c}} = \frac{a}{2} + \frac{b}{4} + \frac{c}{4}$?

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