Puzzle n°4 (*) - Aby or Som, that is the question ! Homepage  


A breeder of abyssinians and somalis, called Roger, had in his house 5 abys and 6 somalis on the ground floor, and 3 abys with 4 somalis on the first floor.

When he woke up at night, Roger used to play the following game: without switching the light on, he would pet a cat in the dark and guess whether it would be a long-haired (a somali) or a short-haired one (an aby). He had a little more chance petting a somali on the first floor than on the ground floor. Because on the ground floor, with 6 somalis among 11 cats, Roger had 54,5% chances of petting one, whereas on the first floor, with 4 somalis among 7 cats, he had 57,1% chances of finding a long-haired one.

three cats

Not very far from his house, lived another breeder of abyssinians and somalis, a young lady named Anita who also had her cats separated in two groups, one on the ground floor with 6 abys and 3 somalis, and another group on the first floor with 9 abys and 5 somalis. And, how surprising, she used to play the same game as Roger at night... And in her home too, to optimize the chances of petting a somali, she had to choose the first floor.
On the ground floor, with 3 somalis among 9 cats, Anita only had 33,3% chances of petting a somali whereas on the first floor, with 5 somalis among 14 cats, the probabilities increased to 35,7%.


And you may guess what happened... One day, side to side in a cat show, Roger and Anita met and fell in love.

They decided to live together happily ever after and bought a large house, with a ground floor and a first floor. They brought their cats in, mixing the "ground floor" cats together on the ground floor of their new home and the "first floor" cats together on the first floor.

When one of them wakes up at night, Roger or Anita still play their old habit of guessing what kind of cat he or she is petting in the dark. In order to optimize their chances of petting a somali, they naturally go upstairs to the first floor ! Are they right ???

... I'm giving up ...


© Marie-Bernadette Pautet, 2005-2019
Last page update: 30.1.2006