Puzzle #40: White-Tailed Cats

This is another puzzle from the same book as I posted last time – “Professor Stewart’s Cabinet of Mathematical Curiosities”. This puzzle appears on Page #31 of the book.

Here is the puzzle:

‘I see you have got a cat,’ said Ms Jones to Ms Smith. ‘I do like its cute white tail! How many cats do you have?’

‘Not a lot,’ said Ms Smith. ‘Ms Brown next door has twenty, which is a lot more than I’ve got.’

‘You still have not told me how many cats yo have!’

‘Well…let me put it like this. If you chose two distinct cats of mine at random, the probability that both of them have white tails is exactly one-half (1/2).’

‘That does not tell me how many you’ve got!’

‘Oh yes it does.’

How many cats does Ms Smith have – and how many have white tails?

Note: for younger children, please avoid the complication of twenty cats, and let them figure out one answer.

As always, please send your answers directly to alokgoyal_2001@yahoo.com and if you like the puzzle, please share it with others. Also, if you have an interesting puzzle that you would like to be posted, please send it to me directly at alokgoyal_2001@yahoo.com

Happy cat-tailing!

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