Priests age

A quick puzzle...

A bell ringer shows three people around the church. They meet the priest, who wants to know the age of the visitors. The bell ringer says, 'The product of their ages is 2450, and the sum of their ages is twice my age'

The priest says, 'I still don’t know'

The bell ringer replies, 'I can tell you that YOU are the oldest of all of us'. To which the priest replies, 'In that case I know their ages'

How old is the priest ?

Alan O'Donnell.

Does this require any knowledge of how old a priest can be before retiring or being ordained?

I can think of six potentially feasible arrangements of ages of the three people, but none help me determin the priests age other than greater than a certain figure.

I suspect, however, there is some trick to the puzle that I'm not seeing.

As the fact that know one is older than the priest appears to be the give-away. The priest must be 49 years old, thus eliminating the second

Make that 50, as the priest appears to be the OLDEST, thus older than all the others... Misread a line

Wrong !!!

Your analysis is perfect, but you picked the wrong one! If the priest is 49, and one of the visitors is 50, the priest cannot be the eldest!

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In other words, the visitors are 5,10,49 and the priest is 50. If the priest was over 50, he still wouldn't know the visitors ages, but as he is exactly 50, this is the only combination it could be!

Correct !

The 'problem' with this is that the priest would have be able to determine the visitor's ages just from knowing product and the sum of the numbers.

If the bell ringer is 36, the priest doesn't need the additional information (that he is the eldest) in order to determine the visitor's ages.

If the bell ringer is 32, this is the only group of visitor ages (up to permutations), so the priest does not need the additional information.

Again, knowing the sum and the product gives a unique solution.

The trick to this problem is that just knowing the sum and the product of the visitors' ages does not uniquely determine the ages. The added information (that the priest is the eldest) is needed to distinguish between two (or more) possible arrangements of the visitors' ages.

(The fact that the sum is twice the bell ringer's age is used in getting that the priest knows the sum of the visitor ages, but tells us in such a way that we do not know the sum of the visitors' ages. While this is not explicitly stated in the problem, the only way I can come up with to solve this problem does presume that the preist already knows the bell ringer's age.)

Brian

So far nobody has demonstrated that 42 is NOT a correct answer.

Bob Bease

BTW: Sorry about the spelling errors in my initial post, a bit too eager to post my answer I suppose.

Then there's insufficient information to reach a solution.

another poster suggested a very peculiar assumption..that the priest can deduce the answer from the fact that he has answered 'I know now'

Actually knowing the bellringer's age is the least wild of other possibilities or assumptions that would be needed to give a solution. But why is this intrinsically better than. 'Oh yeah, you need to assume that Being a priest, God always tells him the answer after one 'I dunno' ' ?

Parsimony??

RJ Pease