Three Silovian mathematicians, Adal, Biru and Cado meet at an actuarial convention. Adal says to the other two, "If you multiply your ages, the product is the year my mother was born."
Biru says, "If you two multiply your ages, the product is the year my mother's mother was born."
Cado says, "If you two multiply your ages, the product is the year my mother's mother's mother was born."
All Silovians know that no Silovian woman has ever given birth younger than 15 nor older than 45.
A fourth mathematician, Diba, arrives and says, "I heard your conversation, but I cannot determine any of your ages."
Adal says, "We all have different ages."
Diba says, "I still can't determine the age of any of you."
What is the most recent year that this convention could have been held?
I made a code with loops and looked for the latest convention date that held the required ambiguities: non-unique solutions for the A and B and C ages found to present the set of possible solutions.
The mother, gmother and ggmother's DOBs are constrained to be betwee (15,45), (30,90) and (45,135) years before a, b, and c's BDs, respectively. Multiple solutions for me begin to crop-up at 1535:
We list:
Year, (a, b, c) bc: (m_min - m_max) ac: (gm_min - gm_max) ab: (ggm_min - ggm_max)
1535 (37,38,39) 1482: (1453-1483) 1443: (1407-1467) 1406: (1361-1451)
1535 (37,39,38) 1482: (1453-1483) 1406: (1406-1466) 1443: (1362-1452)
But "a" is indeed unique in this set. So, it does not work.
But we have yet to consider the fact that a person's age does not unambiguously give their year of birth. Likewise, Solovian mothers may give birth at 45.9 years, so, the whole problem gets very messy including the ambiguity of these non-integer ages and dates. It involves some rather tedious bookkeeping.
And so I, ah, just call it a day and back away slowly...
(The good news is that the additional date ambiguities will allow a more recent conference date solution, one that hopefully does not require Late Middle Age actuaries.)
Edited on October 7, 2023, 5:57 pm
the messiness of non-integer ages
