Friday Puzzler -- What was the puzzle?

Re: Friday Puzzler -- What was the puzzle?

Larry Barrett

Are there multiple answers to this one? I tried a couple of examples that both seem to work. There may be more.

Example 1: Suppose circled numbers are 1, 2, 3, 4. Suppose Cat is 2, Dog is 5 (1 more than 4, a circled number).

5-2 = 3, which is a circled number.

5+2 = 7 which is also equal to 3+4, both circled numbers.

The product of 1x2x3x4x2x5 = 240. The dog's age, 5, is not one of the digits in the product.

Example 2: Suppose the circled numbrs are 1, 2, 3, 5. Suppose the Cat is 1, the Dog is 6 (1 more than 5, a circled number).

6-1 = 5, a circled number.

6+1 = 7 which is also equal to 2+5, both circled numbers.

The product of 1x2x3x5x1x6 = 180. The dog's age, 6, is not one of the digits in the product.

Only one answer

Alex Y

Consider your example 1.

If the circled numbers were 1,2,3,4, I could not have figured out the ages of the dog and cat. As you mentioned, C=2 and D=5 is a possibility. But for the "inner puzzle", so do (C,D) = (1,2), (1,3), (1,4),.... so I wouldn't have been able to determine the cat's and dog's ages.

A computer may help.

Alex Y

In fact, I was not able to solve this one except by brute force, and my creation of a spreadsheet to get it yielded no insights. I was hoping someone else would have a more satisfying solution.

There are 70 possibilities for the four circled numbers

For each of those sets, there are 16 possibilities for the cat's and dog's ages (before testing their sum and difference). Whittling down for the requirements of the sum and difference in the cat's and dog's ages left me with only four sets of circled numbers that had only one solution for the dog and cat, so might have been presented to me allowing me to solve the "inner puzzle" Testing those four with what I revealed about the product of the circled numbers and the cat's and dog's ages gives the set of circled numbers I was shown.