Thought you’d heard the last of the “Cheryl’s birthday” logic question that stumped minds and sparked heated debates all over Singapore? Unfortunately for our poor, overworked brains, the mystery of Cheryl continues — this time involving her age.
Last night, Singapore’s Nanyang Technological University posted Part II of #CherylsBirthday on its Facebook page:
If anything, this puzzle is even more challenging than the last, since it requires factorisation of 144 — a notoriously composite number with 15 factors. The Vulcan Post team racked (and nearly wrecked) our brains to bring you the answer.
The easiest clue to figure out would be in Cheryl’s last sentence — “my brothers have the same age”. This means that in the product of three factors to form 144 (Cheryl’s age x bro’s age x bro’s age), the latter two factors must be the same.
While this narrows down the field, most would have found that there’re still a set of possible answers:
Cheryl’s age x bro’s age x bro’s age:
1 x 12 x 12
4 x 6 x 6
9 x 4 x 4
16 x 3 x 3
36 x 2 x 2
144 x 1 x 1
Sure, it’s probably unlikely that Cheryl is either an infant aged one or an ancient semi-immortal at 144, but math questions aren’t always synonymous with common sense. To narrow down the solutions further, the trick lies in Bernard’s telling statement just before: “Of course we know the bus number, but we still don’t know your age.”
What does this mean? It means that while Albert and Bernard know both the product (144) and sum (bus number) of the three ages, they still can’t narrow down the ages until Cheryl tells them the next clue.
It’s kind of hard to grasp the implications of that, but let us illustrate it for you. In a scenario where the two brothers’ ages must be the same (before Cheryl reveals the last clue), say the ages are E, F and F:
E x F x F = 144
E + 2F = b, a specific sum
Since Albert and Bernard know the sum already, it should be easy for them to figure out what E and F are. The only way they wouldn’t be able to figure it out is if in a scenario where the two brothers’ ages aren’t necessarily the same, this happens (say the ages are H, I and J):
H x I x J = 144
H + I + J = b = E + 2F
So the sum b, whatever it is, has two possible solutions (one where Cheryl’s brothers share the same age, and one where they don’t), with only one answer to our problem.
After much effort, we laid out a spreadsheet of all the possible factors — and their sums — that make up 144:
While there’re a few sums that see repeats, 17 is the only one where the ages of Cheryl’s brothers can be the same, or not — which explains why Albert and Bernard could not solve the question until the last clue was given:
9 + 4 + 4 = 17
And there you have it: Cheryl is 9. That’s one tricky nine-year-old.
We’re by no means 100% sure of this answer, so if you have a different one — or an easier method to solve the problem — let us know in the comments!