Geekery

Test your logic

Posted on 10. Dec, 2009 by Jake.

This week I’ve got logic puzzles that I think you may find interesting to solve. I only got 1 of the 2 correct but maybe you’ll manage to ace them all.

• Why is it better to have round manhole covers than square ones?
• You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won’t get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. What’s the fastest way to make full-sized ice cubes?

Get the solutions next week.

Last week’s solutions:

Problem A: First fill the 5-litre bowl, overspill water from it to fill the 4-litre bowl, which you empty afterwards. Overspill the remaining 1 litre to the 4-litre bowl. Refill the 5-litre bowl and overspill water from it to fill the 4-litre bowl (where there is already 1 litre). Thus you are left with 2 litres in the 5-litre bowl.

Second, the same principle – this time from the other end. Fill the 3-litre bowl and overspill all of the water to the 4-litre bowl. Refill the 3-litre bowl and fill the 4-litre bowl to the top. And there you have 2 litres in the 3-litre bowl.

Problem B: Turn both sand-glasses. After 4 minutes turn upside down the 4-min sand-glass. When the 7-min sand-glass spills the last grain, turn the 7-min upside down. Then you have 1 minute in the 4-min sand-glass left and after spilling everything, in the 7-min sand-glass there will be 1 minute of sand down (already spilt). Turn the 7-min sand-glass upside down and let the 1 minute go back. And that’s it. 4 + 3 + 1 + 1 = 9

You can find more water and weighing puzzles at http://brainden.com/weighing-puzzles.htm

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Riddle me this…

Posted on 01. Dec, 2009 by Jake.

This week’s riddles are actually quite easy so go on, have a stab at the following.

Problem A

How would you measure 2 litres of water if you had:

1. 4 and 5-liter bowls
2. 4 and 3-liter bowls?

Problem B

If you have 2 sandglasses: one 7-minute and the second one 4-minute, how can you correctly time 9 minutes?

Answer to last week’s riddle:

The Empty Triangle

Which figure should be placed in the empty triangle?

The top number minus the bottom left-hand number is multiplied by the bottom right-hand number to give the number inside the triangle.

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The Empty Triangle

Posted on 16. Nov, 2009 by Jake.

This week’s brain teaser is just for the ubergeeks. I’m taking it up a notch to see if you can reveal your true geekery or if you’re just a plain novice in a Think Geek t-shirt. FYI -This puzzle happened to be found in a Mensa publication.

Question:

Which figure should be placed in the empty triangle?

Catch the solution to this brain teaser right here next Mon, 23 Nov 2009.

Answers to last week’s riddle:

Question 1:
What do the following numbers have in common?
3    7    10    11    12
Answer:
The only vowel they contain when written out fully is the letter E.

Question 2:
What is the next number in this series?
5   25   61   113   181   ..
Answer:
265. The series consists of the sums of the squares of 1 and 2, 3 and 4, 5 and 6, etc

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Riddles: The King, The Emperor, and The Magician

Posted on 07. Oct, 2009 by Jake.

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?

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?

Solutions for The Really, Really, Really Big Number:

The Really, Really Big Number

Solution:
1

Explanation:
This one is so sneaky.

First, consider 100 divided by 11.  The remainder here is 1.  Now consider the remainder when 100×100 is divided by 11.  Don’t do it on your calculator or on paper.  Rather, consider that you have one hundred hundreds, and each of them has a remainder of 1 when divided by 11.  So, go through each of your hundred hundreds and divide it by 11, leaving remainder 1.  Then collect up your remainders into a single hundred, and divide it by 11, leaving a remainder of 1.  This process can be extended to dividing 100×100x100 by 11, and indeed, to dividing any power of 100 by 11.

The Unkindest Cut of All, Part 1 of 2

Solution:
12.5

Explanation:
I am especially fond of these two ways to solve this problem:

1. Draw the right triangle whose hypotenuse is the square’s diagonal, and whose two legs are two sides of the square.  Then use the Pythagorean Theorem (a^2 + b^2 = c^2) to solve for the length of each side.  Since two sides are equal, we get (a^2 + a^2 = c^2), or (2(a^2) = c^2) ).  Since c is 5, 2(a^2) = 25, making a^2 equal to 25/2, or 12.5.  Since the area of the square is a^2, we’re done: it’s 12.5.

2. Tilt the square 45 degrees and draw a square around it such the the corners of the original square just touch the middles of the sides of the new, larger square.  The new square has sides each 5 units long (the diagonal of the smaller square), and it therefore has area 25.  However, a closer inspection reveals that the area of the larger square must be exactly twice that of the smaller.  Therefore the smaller square has area 25/2, or 12.5.

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Riddles: phone numbers and test yourself

Posted on 05. Aug, 2009 by Jake.

Riddle: phone numbers

There is a town in Texas where 5% of all the people living there have unlisted phone numbers. If you selected 100 names at random from the town’s phone directory, on average, how
many of these people would have unlisted phone numbers?

 Answer: None. You will not find unlisted phone numbers in a phone directory.

Riddle: mental test

It doesn’t hurt to take a hard look at yourself from time to time. This little test should help you get started.

During a visit to a mental asylum, a visitor asked the Director what the criteria is that defines if a patient should be institutionalized.

“Well,” said the Director, “we fill up a bathtub. Then we offer a teaspoon, a teacup, and a bucket to the patient and ask the patient to empty the bathtub.”

Okay, here’s your test:
1. Would you use the spoon?
2. Would you use the teacup?
3. Would you use the bucket?

“Oh, I understand,” said the visitor. “A normal person would choose the bucket, as it is larger than the spoon.”
What was the director’s response?

Answer: ”No,” answered the Director. “A normal person would pull the plug.”

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