** problem:** In a certain game, 30 balls of k, different colours are kept inside a sealed box .You are told only the value of k,but not the number of balls of each colour . Based on this, you have to guess whether it is possible to split the balls into 10 groups of each, such that in each group the three balls are of different colours.Your answer is to be a simple YES or NO.You win or loss a point according as your guess correct or not.For what values of k, you can say NO and be sure of winning?For what values of k, you can say YES and be sure of winning?Justify your solution.

**Solution:** No & sure of winning :- 1,2.

* Justification: *If colours are there the 3 balls cannot be of different colours & if \({{k} \ge {3}} \) then there exists a possibility of splitting into two groups of 3 each in each group 3 balls are of different colours.

For k = 3 take 10 ball of each colour & the splitting is possible.

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