Solution to Puzzle #40: White-Tailed Cats

Two children sent me correct answers this time. Like last time, Shruti Mittal (from Mumbai) was the first one to send me a correct answer, and Danny Mittal (from Virginia, USA) also sent me a correct answer. Very well done!

The actual answer requires one to get into a bit of algebra and combinatorial mathematics, the intent of the puzzle was for people to solve this more intuitively. Key to solving was the following:

– If you have c cats, then the number of ways in which you can select 2 cats is c * (c-1)

– If w are white tailed, then the number of ways in which one can select two white tailed cats are w * (w-1)

Since we are looking for a chance of 1/2 for selecting both white tailed cats, quick intuitive thought process will lead to the answer of a total of 4 cats, with 3 of them being white tailed.

The reason the figure of <=20 was also given in the puzzle was that the next possible answer is #cats = 21, and #white tailed cats = 15, which also has the probability of 1/2 for selecting two white tailed cats at random.

Hope you enjoyed the puzzle!


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