The Bus Conversation
Pingy and Neal arrived at work in the Puzzlarian Puzzle Factory. Enjoying their first cup of coffee, the following conversation insued:
Pingy: "This morning on my bus ride to work, there were only three other passengers and I knew everyone on the bus. During the ride, one of them mentioned ages, and I mentally figured that the product of their ages was 2,450 ... and if I totaled the ages, the sum was twice your age. How old were the three passengers?"
Neal: "Wait a minute ... you haven't supplied enough information!"
Pingy: "Oh yeah, I forgot to tell you that one of the passengers was older than I am, which is ...."
Neal: "Yeah, I know how old you are. And now I also know how old each of the passengers were ... they were __ , __ , and __ years of age."
Complete Neal's last statement.
Also, how old are Pingy and Neal?
Pingy: "This morning on my bus ride to work, there were only three other passengers and I knew everyone on the bus. During the ride, one of them mentioned ages, and I mentally figured that the product of their ages was 2,450 ... and if I totaled the ages, the sum was twice your age. How old were the three passengers?"
Neal: "Wait a minute ... you haven't supplied enough information!"
Pingy: "Oh yeah, I forgot to tell you that one of the passengers was older than I am, which is ...."
Neal: "Yeah, I know how old you are. And now I also know how old each of the passengers were ... they were __ , __ , and __ years of age."
Complete Neal's last statement.
Also, how old are Pingy and Neal?
posted by Zaux at
5:20 AM
7 Comments:
Is the driver counted in the total product or sum?
7, 10, and 35.
Neal: 26
Pingy: 34
If I figured this one out, you need a result in which you can have 2 or more different combinations that both make the product 2450 and sum - double Neal's age, since he couldn't figure it out before I told him someone's older than me.
With the 7,10,35 combination, Pingy does not HAVE to be 34. He could be as young as 26 and Neal would still know.
But another combination that works is 2, 25, 49, with Pingy=38 and Neal anything from 26 to 48.
Since there is ambiguity here, we MUST make Neal at least 36-48 and use the 2,25,49 combination.
Passengers: 2, 25, 49
Pingy: 38
Neal: at least 36, no more than 48
Alright I'm pretty sure I got this now (Bit of trial and error, bit of maths :P):
The only 2 combinations with same sum are 5 - 10 - 49 and 7 - 7- 50, making both sums 64 and Neal's age 32. It couldn't have been enough information before, because as already mentioned, both sum up as double Neal's age. Since we now know that one was older than me, it has to be 7 - 7 - 50 making me 49 (Because if I was any other age, both could be valid, or for that matters, just about every other combination (of course not something like 1 - 1 - 2450)). So yeah, my answer here is:
I'm 49, Neal is 32 and the passengers are 50 and two of them are 7.
Anyway, there could be, but I doubt it, another solution, but this seems to be correct. Even if there's another, this still is valid :P
Ross: Neal is exactly half the sum, so it can't be anything from-to :)
PS: No, I'm not really 49 :P
Good job Pingy ...
you win a free ride on the Puzzlarian bus service. :)
Sorry I would of posted but that would of been cheating (insider information and all).
Ha ha glad to see my name in a puzzle. =)
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