Just noticed this wasn't solved till now. Sorry zeogold, I made you come up with it then when you did it somehow slipped me :(

Here goes:

Writing equations from the information given

(b-c)*4 = f-c
b*3 = u
c*4 = f
(c+4)*4 = u+4

Four linear equations with four unknowns.

Solving:

c=9.6
b=16.8
f=38.4
u=50.4

So.
Cousin is 9.6 years old, brother is 16.8, father is 38.4, uncle is 50.4.

WWhen cousin was born (9.6) years ago, his brother was 7.2, exactly one quarter of the fater who was 28.8 then.
Brother now is third of the age of his uncle.
Cousin now is quarter of the age of the father.
In four years, the cousin will be 13.6, exactly one quarter of the age of his uncle, who will be 54.4 then.
Like the "all horses are of same colour..."

Anyway, go ahead and ask your puzzle now since you answered first. Otherwise, I'll come up with something myself.

It's alright. At this point, I'm fairly used to my puzzles getting minimal activity.
You're on the right track, but your numbers are too high.

How so? They fit exactly with all your constrainsts:

When cousin was born (9.6) years ago, his brother was 7.2, exactly one quarter of the fater who was 28.8 then.
Brother now is third of the age of his uncle.
Cousin now is quarter of the age of the father.
In four years, the cousin will be 13.6, exactly one quarter of the age of his uncle, who will be 54.4 then.

And since these are linear equations with 4 unknowns, no other numbers will fit.

What are your answers?

Maybe I wrote the puzzle incorrectly, but the answer should have been 8.25.

OK, now I see you've written "in the year" which means 8.25 should be rounded, but you don't give info on what month it is now, so we don't know whether it should be up or down. This changes things a bit.

"My cousin is as quarter as old as his dad."
Therefore Dad is 8.25 * 4 = 33

"In four more years, he'll be a quarter as old as his uncle will be!"
In four years. Cousin will be 12.25. Uncle will be 12.25 * 4 = 49.
Therefore uncle now is 45

"and now this brother is a third of the age of his uncle. "
Brother is now 15

"In the year in which he was born, his brother was exactly one quarter of the age of their father"
If the cuerrent month is April onwards, then it means that "the year in which the cousin was born" was 8 years ago, in which case the father was 25 and brother 7, not a quarter. If it was Jan to March, in that case you're right, when the cousin was born it was 9 years ago, and the father and brother were 24 and 6 respectively.

If we take the month in which you originally posted it as "now" then your answer is correct. But your answer will only work in the first quarter of the year ;)

Basically given your original wording, the puzzle has infinitely many answers, but some of them working only if "now" is within a certain day of the year (in your case, it's the first quarter). My answer is the only one which would work all year round.





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Anyway, no need to keep this thread artificially alive, but if anyone has any interesting maths puzzle post it here. If I come across anything I'll bump this.

This? A math test, but anyway...

Here's one that I have not been able to solve, so I do not know what the correct answer is (and I do not know if it has been solved in the first place).

Earlier in the thread, I mentioned Moser's number and asked what the least significant digit was (a problem that is pretty easy if you know what you're doing and can recognize patterns). However, there is a similar problem that isn't so easy:

What is the *most* significant digit of Moser's number? In other words, the digit on the far left?

For extra credit, answer the same question about Graham's number as well.

Note that I will not accept an answer that lacks proof, particularly since I actually do not know the answer in the first place, and there aren't enough computing resources in the universe to brute force the answer.

3 and 7, respectively. If you think about it for a minute, I'm sure you can see why.

Sorry, but that doesn't count. I need an actual proof in order to consider your answer.