Geekery

Oldest Piano Player on a Railroad Bridge Riddle

Posted on 21. Aug, 2009 by Jake in brain teasers

Think you’re fast? Time yourself solving these riddles, submit your time in the comments section (…those who tell the truth get a noddy badge!)

The Oldest Plays the Piano

Two MIT math grads bump into each other while shopping at Fry’s. They haven’t seen each other in over 20 years.

First grad to the second: “How have you been?”
Second: “Great! I got married and I have three daughters now.”
First: “Really? How old are they?”
Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there…”
First: “Right, ok… Oh wait… Hmm, I still don’t know.”
Second: “Oh sorry, the oldest one just started to play the piano.”
First: “Wonderful! My oldest is the same age!”

How old was the first grad’s daughter?

Answer:

The possible ages ( factors of 72 ) and their sums are shown below:
Ages:            Sum of ages:
1 1 72            74
1 2 36            39
1 3 24            28
1 4 18            23
1 6 12            19
1 8 9             18
2 2 18            22
2 3 12            17
2 4 9             15
2 6 6             14
3 3 8             14
3 4 6             13

We can deduce from the man’s confusion over the building number that this wasn’t enough information to solve the problem. The chart shows the sum 14 twice for two different age possibilities, which would explain how knowing the building number alone would not have given him the answer. The clue that the “oldest one” started to play the piano rules out “2 6 6” as an answer, because there is no “oldest”. Since the first grad was certain with the piano clue, the first grad’s oldest daughter is 8. I’ll leave it up to the reader to figure out why this doesn’t necessarily mean the second grad’s oldest daughter was also 8.

Railroad Bridge

A man needs to go through a train tunnel.  he starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him.  You don’t know how far away the train is, or how fast it is going, (or how fast he is going).  All you know is that:

1. if the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the train hits him,
2. if the man keeps running through the tunnel, he will also just barely make it out of the tunnel alive before the train hits him.

Assume the man runs the same speed whether he goes back to the start or continues on through the tunnel.  Also assume that he accelerates to his top speed instantaneously.  assume the train misses him by an infintisimal amount and all those other reasonable assumptions that go along with puzzles like this so that some wanker doesn’t say the problem isn’t well defined.

How fast is the train going compared to the man?

Answer:

We know that the train and man will reach the start of the tunnel at the same time if the man turns around, in that time the man travels 1/4th the length of the tunnel. 

If the man travels on towards the end of the tunnel he will be able to travel an additional 1/4th of the length of the tunnel before the train reaches the start of the tunnel, putting the man at the half way point.

For both the man and the train to reach the end of the tunnel at the same time, the man has to travel 1/2 the length of the tunnel while the train has to travel the full length of the tunnel.

Therefore the train must be travelling twice as fast as the man (and as an aside must have been half the length of the tunnel away from the start of the tunnel when it blew its whistle).

Tags: brain teaser, geekery, maths, MIT, piano, railroad bridge, riddle