Inspired by Inspired by Me

Probability Level 5

∑ 1 ≤ x , y , z ≤ 10 max ⁡ ( x , y , z ) = ? \large \sum_{1\leq x,y,z \leq 10} \max(x,y,z) =\, ?

The sum is over all ordered triples ( x , y , z ) (x,y,z) of integers between 1 and 10 (inclusive).

Recursive inspiration .


The answer is 7975.

Arjen Vreugdenhil by Arjen Vreugdenhil , 44, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Arjen Vreugdenhil
Mar 30, 2016

If you did this problem , it is easy: ∑ max ( x , y , z ) = ∑ ( 11 − min ( 11 − x , 11 − y , 11 − z ) ) = 1 0 3 ⋅ 11 − ∑ min ( x , y , z ) . \sum \text{max}(x,y,z) = \sum (11-\text{min}(11-x,11-y,11-z)) = 10^3\cdot 11 - \sum \text{min}(x,y,z). So, figure out the other problem, then subtract from 11 000 11\:000 .

6 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...