Geekery

Riddles: Your Number’s Up

Posted on 04. Nov, 2009 by Jake.

Things are getting trickier as the year comes to it’s inevitable and less than graceful close. Ain’t it feel good that in this crazy world some things – maybe not the weather in Jo’burg, but some things – always make sense. That is, if you can figure ‘em out

Riddle 1 for the week

What do the following numbers have in common? (tricky one, this…)
3    7    10    11    12

Riddle 2 for the week

What is the next number in this series?
5   25   61   113   181   ..

Answers to be put up on the 16th of November.

Answers to last week’s riddles:

Problem 1:
Take the letters ERGRO. Put three letters in front of it, and the same three letters behind to form a common English word.
UND(ERGRO)UND

Problem 2:
Which of the following words is the
odd-one-out?
IBIS IBEX ORYX SIKA ZEBU
Ibis is a bird the rest are mammals

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Riddles: Word Up

Posted on 27. Oct, 2009 by Jake.

Today’s riddles are all simple, short and to the point…. the point being, they’re word problems!

Problem 1:

Take the letters ERGRO. Put three letters in front of it, and the same three letters behind to form a common English word.

Problem 2:

Which of the following words is the odd-one-out?

IBIS IBEX ORYX SIKA ZEBU

Answers to Palindrome’s and Maths:

A car”s odometer shows 72927 miles a palindromic number. What are the minimum miles you would need to travel to form another?”
Answer
110 miles. (73037)

Question
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?
Answer
$45. The pricing method consists of charging $5 for each letter required to spell the item.

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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: Band on a Bridge

Posted on 07. Sep, 2009 by Jake.

More puzzles for ya today…

Band across the Bridge
Four members of a band are walking to a night concert. They decide to take a shortcut, but must cross a bridge. Luckily they have one flashlight. Because of the varying size of their instruments, it takes each member a different amount of time to cross the bridge – it takes the first person one minute, the second person two minutes, the third person five minutes and the fourth person ten minutes. They must cross the bridge in pairs, travelling at the slower speed so if the one minute person went with the ten minute person, it would take a total of ten minutes. Since there is only one flashlight, one person must come back across the bridge, then another pair can cross. They only have 17 minutes to cross the bridge and still get to the concert on time. What order should they cross to get everyone across and get to the concert?

Answer: First, the one minute person and the two minute person must cross the bridge, for a total of two minutes. Then the one minute person should come back with flashlight – total of three minutes. The five minute person and the ten minute person cross together next, making the total thirteen minutes. Now the two minute person goes back and (total now fifteen minutes) and gets the one minute person and they cross together bringing the total to seventeen minutes.

Weighing for Godot
Godot was recently hired by a local shipping factory and was struggling to read the labels. He could read the weights, but not the addresses. Before he could decipher the text, a pair of brothers walked in and declared that some of the six boxes currently sitting on the counter belonged to them. Godot asked if they knew which ones were their packages, but the first brother only knew that his packages weighed twice what his brother’s two did. If the packages weighed 15, 16, 18, 19, 20, and 31 pounds, which packages did Godot hand them?

Answer:

brother one = 31lb+ 19lb+ 16lb = 66 lbs.
brother two = 18lb + 15lb = 33lb 33lb x 2 = 66 lbs.

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Riddles: Fuses and filling barrels

Posted on 25. Aug, 2009 by Jake.

Riddle – burning fuses

You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can’t measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?

Answer: Two half-full barrels are dumped into one of the empty barrels. Two more half-full barrels are dumped into another one of the empty barrels. This results in nine full barrels, three half-full barrels, and nine empty barrels. Each son gets three full barrels, one half-full barrel, and three empty barrels.
You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can’t measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?

Riddle – wine in barrels

A man is the owner of a winery who recently passed away. In his will, he left 21 barrels (seven of which are filled with wine, seven of which are half full, and seven of which are empty) to his three sons. However, the wine and barrels must be split so that each son has the same number of full barrels, the same number of half-full barrels, and the same number of empty barrels. Note that there are no measuring devices handy. How can the barrels and wine be evenly divided?

Answer:

Light one fuse at both ends and, at the same time, light the second fuse at one end. When the first fuse has completely burned, you know that a half hour has elapsed, and, more relevantly, that the second fuse has a half hour left to go. At this time, light the second fuse from the other end. This will cause it to burn out in 15 more minutes. At that point, exactly 45 minutes will have elapsed.

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