###T A R O T R E A D E R L O G I C A S S E S S M E N T === ###1). What were the weights of the cats? *** The weights of the cats were 1 kilogram, 6 kilograms, and 6 kilograms.
###2). How did you arrive at that answer? Show your process.
Initially, I felt that every piece of information must give some clue as to the answer. Was it significant that the woman was a tarot card reader, or that she was located on 15th? How did the headache fit in to the answer? I also challenged information given and not given. Were these domestic cats, or could they be larger, perhaps bobcats or baby tigers? Were all three cats separate, or was it possibly a pregnant mother carrying twins? Could any of the cats be inanimate?
Feeling satisfied that I had adressed most possible tricks, I began to tackle the problem logically.
First, I gathered what seemed to be the most significant facts:
- There are three cats.
- Each is weighed in whole kilograms.
- The weight of each multiplied together is 36.
- The added weights are the same as the price of the tarot reading.
- Knowing the price of the tarot reading leaves the answer vague.
- All doubt is removed when Bookis sees the smallest cat.
Second, I wrote out all of the possible permutations that would multiply to 36 (along with corresponding sums):
- 1 x 1 x 36 (adds to 38)
- 1 x 2 x 18 (adds to 21)
- 1 x 3 x 12 (adds to 16)
- 1 x 4 x 9 (adds to 14)
- 1 x 6 x 6 (adds to 13)
- 2 x 2 x 9 (adds to 13)
- 2 x 3 x 6 (adds to 11)
- 3 x 3 x 4 (adds to 10)
Third, I took into account the fact that knowing the price of the reading did not make the answer clear:
Since the weights were still in question, there must be more than one solution that would match the the cost of a reading. Since there is only one sum that occurs more than once, that leaves us with:
- 1 x 6 x 6 (adds to 13)
and
- 2 x 2 x 9 (also adds to 13)
Finally, since learning that there is a smallest cat convinces Bookis of the answer, we know that the answer is 1, 6, and 6:
Finding that there is a "smallest" cat implies that the the two smallest cats are not of equal size. If the cat had been 2 kilograms, it is highly unlikely (though perhaps not impossible) that it would be called the "smallest." But any doubt is removed when Bookis sees the size of the cat. Seeing the tiny cat reassures him that he is correct in assuming that the cats are 1, 6, and 6 kilograms.
###3). What other possible answers are there?
There is only one other remote possibility. We assume that the smallest cat is in fact smaller than (and not equal in size to) any of the other cats. However, if this assumption is incorrect, then it is possible that the cats' weights could be 2, 2, and 9 kilograms.