A box contains five set of balls while there are three balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainly that a

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Submitted by examrobotsa on

Q: 69 (IAS/2006)
A box contains five set of balls while there are three balls in each set. Each set of balls has one colour which is different from every other set. What is the least number of balls that must be removed from the box in order to claim with certainly that a pair of balls of the same colour has been removed?

question_subject: 

Logic/Reasoning

question_exam: 

IAS

stats: 

0,5,6,5,3,3,0

keywords: 

{'balls': [0, 1, 1, 0], 'least number': [0, 0, 1, 0], 'same colour': [0, 0, 6, 0], 'other set': [0, 0, 1, 0], 'colour': [11, 6, 13, 28], 'pair': [7, 0, 1, 12], 'box': [0, 0, 3, 3], 'order': [6, 12, 34, 35], 'set': [1, 2, 1, 0]}

Alert - correct answer should be 6.

Here`s why - There are five sets of balls and each set is of a different color. If you want to ensure that you`ve picked at least two balls of the same color, you need to look at the worst-case scenario. The worst-case scenario would be that you pick one ball, and it is of a unique color. Then you pick a second ball and it is of a second unique color. This scenario continues until you have picked one from each of the five sets. So, with five picks, you still don`t have a pair of the same color. On the sixth draw, however, you`re guaranteed to have a pair since you`ve already picked a ball from each set, so anymore picking ensures a duplicate color. Thus, the correct answer should be 6, not 1. The provided answer is not accurate.