Bookis had had a splitting headache for days. He had tried everything he could think of to get some relief and nothing was working. He asked his mother for advice. She said, “go visit the tarot card reader on 15th and he’ll know just the cure.” Bookis was skeptical but desperate, so he decided to give it a shot. Upon entering the store, the tarot card reader said, “You’ve got a headache. I’ve got a potion to cure you, but you’ll have to guess the weights of my three prized cats (in whole kilograms).” Bookis said he was game, but that he needed a hint. The tarot card reader said, “If you multiply the weight of each, you get 36.” Bookis thought for a moment and said, “I need another hint.” The tarot card reader said, “If you add their weights, it's the same as the price of a tarot reading.” The tarot reader pointed at the board behind the counter with the price list. Bookis looked up at the board and said, “Okay, I see the price, but I still don’t have enough information to answer definitively - can you give me just one more hint?” The tarot reader said, “I can’t give you a hint, but Sammy, my littlest kitty, really seems to like you!” The cat chewed on Bookis’s sleeve. At that point, Bookis exclaimed “I know the weights of your cats!” Bookis told the tarot reader the weights, got his headache potion (which worked immediately), and pet Sammy’s head before leaving.
1. What were the weights of the cats?
Most likely the weights were 1, 6, and 6 kilograms.
2. How did you arrive at that answer? Show your process.
The weights of the cats can not be definitively solved by the information that was given, but I can come up with an educated guess. I created a list of integers that, if multiplied together, gives you 36 ( A x B x C = 36):
1 x 1 = 36
1 x 2 = 18
1 x 3 = 12
1 x 4 = 9
1 x 6 = 6
2 x 2 = 9
2 x 3 = 6
3 x 3 = 4
and since the question said their sum equals the price of the reading I did the math (even though it seemed like this bit of information was useless… at the time).
1 + 1 + 36 = 38
1 + 2 + 18= 21
1 + 3 + 12= 16
1 + 4 + 9 = 14
1 + 6 + 6 = 13
2 + 2 + 9 = 13
2 + 3 + 6 =11
3 + 3 + 4 = 10
Bookis saw the price yet still needed another clue…. so upon evaluating the sums, I saw two combinations( 1,6,6 and 2,2,9) add up to the same number (13). This must be why he needed just one more clue to help differentiate them apart. The tarot reader referred to Sammy as the “littlest kitty,” which implies one cat is lighter than the rest. With this information, I eliminated 2, 2, and 9.
3. What other possible answers are there?
Sammy may not have been one of the three prized cats, meaning that 2, 2 and 9 would have been acceptable weights; however, since Bookis knew the weights after this hint, I suspect Sammy was indeed one of the prized cats.
Another idea I had, is to eliminating the extreme and unreasonable weights, by finding the average weight range, taking into account standard deviation. Using Google I found four common breeds of cats: domestic, siamese, persian, and coon. Then, I averaged the weights using the four breeds. The results are as follows: the avg lightest weight equals 3kg with a standard deviation of 1.0 and heaviest 6kg with a standard deviation of 3.0, all rounded to the nearest integer. Using this information, 2- 4kg was my cut off range for lightest and 3- 9kg for heaviest. I, again, eliminated combinations that contained the same smallest integer because of Sammy, leaving only 2, 3, and 6. Refference