Geekery

Riddles, Palidromes, and Maths.

Posted on 15. Oct, 2009 by Jake.

Brainteasers for the week

The Palindromic Car Odometer

A car’s odometer shows 72927 miles a palindromic number. What are the minimum miles you would need to travel to form another?

Pricing the Clothing Sale

There is a clothing store in Bartlesville. The owner has devised his own method of pricing items. A vest costs $20 socks cost $25 a tie costs $15 and a blouse costs $30. Using the method how much would a pair of underwear cost?

Answers for

The King, The Emperor, and The Magician:

Life or Death? The Emperor’s Proposition
You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, “Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you and mix the bowls around. You then can choose one bowl and remove ONE marble. If the marble is WHITE you will live, but if the marble is BLACK… you will die.”

How do you divide the marbles up so that you have the greatest probability of choosing a WHITE marble?

Answer
Place 1 white marble in one bowl, and place the rest of the marbles in the other bowl (49 whites, and 50 blacks).

This way you begin with a 50/50 chance of choosing the bowl with just one white marble, therefore life! BUT even if you choose the other bowl, you still have ALMOST a 50/50 chance at picking one of the 49 white marbles.

Knights of the Round Table
King Arthur, Merlin, Sir Lancelot, Sir Gawain, and Guinevere decide to go to their favorite restaurant to share some mead and grilled meats. They sit down at a round table for five, and as soon as they do, Lancelot notes, “We sat down around the table in age order! What are the odds of that?”

Merlin smiles broadly. “This is easily solved without any magic.” He then shared the answer. What did he say the odds were?

Answer
The odds are 11:1. (The probability is 1/12.)

Imagine they sat down in age order, with each person randomly picking a seat. The first person is guaranteed to pick a seat that “works”. The second oldest can sit to his right or left, since these five can sit either clockwise or counterclockwise. The probability of picking a seat that works is thus 2/4, or 1/2. The third oldest now has three chairs to choose from, one of which continues the progression in the order determined by the second person, for a probability of 1/3. This leaves two seats for the fourth oldest, or a 1/2 chance. The youngest would thus be guaranteed to sit in the right seat, since there is only one seat left. This gives 1 * 1/2 * 1/3 * 1/2 * 1 = 1/12, or 11:1 odds against.

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Riddles: The Really, Really, Really Big Number

Posted on 16. Sep, 2009 by Jake.

The Really, Really, Really Big Number

When you divide 12 by 5, the remainder is 2; it’s what’s left over after you have removed all the 5s from the 12.  When you raise 4 to the fifth power (that is, 45), you multiply four by itself five times: 4×4×4×4×4, which equals 1,024.

What is the remainder when you divide 100100 by 11?

The Unkindest Cut of All, Part 1 of 2

The area of a square is equal to the square of the length of one side. So, for example, a square with side length 3 has area (32), or 9. What is the area of a square whose diagonal is length 5?

Answers will be published on Tuesday the 29th of September

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Oldest Piano Player on a Railroad Bridge Riddle

Posted on 21. Aug, 2009 by Jake.

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).

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