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Logical Puzzles Medium 3 min

A box contains red, blue and green balls. There are more red balls than blue balls and more blue balls than green balls. If there are 9 balls in total and each color has at least one ball, how many possible distributions are there?

Hint
Let red > blue > green and add the three counts.

Answer

3 distributions.

Explanation

The positive integer triples satisfying red > blue > green and summing to 9 are (6,2,1), (5,3,1), and (4,3,2).

Step-by-Step Solution

6+2+1=9.
5+3+1=9.
4+3+2=9.
No other strictly decreasing positive triples sum to 9.
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