A Riddle a Day -- 78 Logical and Mathematical Puzzles

Weekend Solution

Based on the first clue, factorizing the number 36 would be essential to solving the riddle:

The triplet factors for 36 are:

1 * 2 * 18

1 * 3 * 12

1 * 4 * 9

1 * 6 * 6

2 * 2 * 9

2 * 3 * 6

3 * 3 * 4

1 * 1 * 36

The second clue tells us that the sum of the children's ages is important. So next the factors must be added up:

And their sums are:

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

1 + 1 + 36 = 38

At this point, something about the sums stands out: All but two of them are unique. If the two logicians had shared an apartment numbered 21, 16, 14, 11, or 10, then the guessing logician would have all the information he needs to guess the ages of his friend's children. The fact that he requires a third hint tells us the two logicians lived in Apartment #13 - the only non-unique sum:

1 + 6 + 6 = 13

2 + 2 + 9 = 13

The third clue tells us which factorization is accurate. It has to be the factorization that allows for an unambiguously eldest child. The children's ages are therefore 9, 2, and 2.

Theological Challenge Solution

The question to prove the statement wrong would be: Is this always true? Done. That automatically negates the statement. @PiMaster got this one right! great job!

Don't forget to go check out the solution to Day 41's riddle and vote! (No one solved it, but @PiMaster was close).