# Web Puzzles

Showing posts with label riddles online. Show all posts

## Switching Logic

You are in a basement. In front of you are three light switches, all in their OFF state. These switches are connected to three lightbulbs that are on a wall in the attic, so there's no chance you can see them unless you climb the stairs all the way up. There is a 1-to-1 mapping between the switches and the bulbs.

You are given plenty of time to play around with the switches in the basement, where you can put each individual switch in either its ON or OFF state.

However, you can only go upstairs once to check on the state of the bulbs!

Once you've gone upstairs and checked on the bulbs, you must be able to tell with 100% certainty which bulb is connected to which switch, without having to go down again.

How can you tell which switch is connected to each bulb?

Notes:
• You can't put a switch halfway between ON and OFF, hoping that this would make the bulb flicker like a bad neon light...
• You can't control the switches from a distance, eg with a string or whatever other form of remote control.
• You can't have anyone cooperating with you on the other floor, and that includes your dog who knows how to bark once for a 'yes' and twice for a 'no'.

### Switching Logic Puzzle Solution

Turn switch #1 ON. After about five minutes or so, turn switch #1 OFF and turn switch #2 ON.
Then go upstairs and check on the bulbs.

The one ON is obviously #2. The other ones are OFF, but one of them should be very hot by having been ON for five minutes. That's #1, and the remaining bulb is #3.

## Boxes, Beads, and a Blindfold

You have been named as a traitor by the King, the punishment for this crime is death. Although he is a cruel tyrant he gives you one last chance at freedom. When you are finally brought before him he has this to say to you:

"There are 100 beads, 50 black and 50 white. You will be allowed to draw one bead, whilst blindfolded of course. If it is black you will be condemned to death, if it is white you will be set free".

So far so good you think to yourself, at least I have a 50/50 chance.

"The beads will be distributed amongst four boxes by me," he continued. "You must select a box by opening it, draw one bead from it and then present the bead to the court. Thus will your fate be decided".

Upon saying this a cruel smile appears on the King's face and you suddenly break into a cold sweat as you remember that the King is both very wicked and devilishly cunning.

Assuming that the King is incredibly smart, evil, thinks that you are a stupid, uneducated peasant and wants to minimise your chance of freedom, what strategy should you employ, and what is the probability of surviving?

Notes:
• The King whilst evil won't cheat.
• The trick is to work out how he plans on distributing the beads to minimise your chance of success.
• As soon as you stick your hand in one of the boxes you must draw a bead from it.
• The boxes and beads light and portable, however you are not allowed to remove them from the area.
• The King thinks you are stupid.

### Boxes, Beads, and a Blindfold Puzzle Solution

The king puts 1 black bead in 3 of the 4 boxes and all the other beads (both black and white) in the fourth box.

In the kings' view, you will just randomly pick a box because you are so stupid. This gives you barely 1 chance out of 8 to pick a white bead (1/4 to pick that one box containing white beads multiplied with almost 1/2 to pick a white bead out that box).

Assuming each of the four boxes are identical, by picking up each box in turn, you will be able to tell by weight or the rattling noises which one of the boxes contains the mixed beads. Picking the box with the mixed beads will mean that you have a slightly better than 50% chance of living.

Thanks to "Ben Leil" and "Kobold" for posting solutions in the forum

## The Geneaology

Tom and Tim, time tested twice troublesome twins, entered the kitchen at ten o'clock on a Tuesday evening. "Mom, mom, look what I found" said Tom, waving a sheet of faded paper.

"No, I found it." said Tim.

"What is it, Tom?" Mom asks.

"I don't know, mom, but it talks about Genies."

"really?" she replied as she took the paper from him. It was a copy of the family geneaology she had been looking for so she could do some research. "where was it?"

"It was in that Bible on the mantle." said Tim, "Between page 588 and 589."

"No," said Tom, "it was between pages 1201 and 1202!"

Mom gave Tom a dirty look, and said to Tim, "thanks for finding this sweetie." She looks at Tom.

"Why did you lie to me, Tom?"

How did Mom know that Tom was lying?

### The Geneaology Puzzle Solution

Page 1 in a book is the page just inside the front cover. Page 2 is the other side of the same sheet.

Pages 1201 and 1202 are opposite sides of the same sheet of paper, so finding something between these two is highly improbable.

## Strawberry Ice Cream

A man walks into a bar, orders a drink, and starts chatting with the bartender.

After a while, he learns that the bartender has three children. "How old are your children?" he asks.
"Well," replies the bartender, "The product of their ages is 72."

The man thinks for a moment and then says, "That's not enough information."

"All right," continues the bartender. "If you go outside and look at the building number posted over the door to the bar, you'll see the sum of the ages."

The man steps outside, and after a few moments he reenters and declares, "Still not enough!"

The bartender smiles and says, "My youngest just loves strawberry ice cream."

How old are the children?

### Strawberry Ice Cream Puzzle Solution

First, determine all the ways that three ages can multiply together to get 72:
• 72 1 1 (quite a feat for the bartender)
• 36 2 1
• 24 3 1
• 18 4 1
• 18 2 2
• 12 6 1
• 12 3 2
• 9 4 2
• 9 8 1
• 8 3 3
• 6 6 2
• 6 4 3
As the man says, that's not enough information; there are many possibilities.

So the bartender tells him where to find the sum of the ages--the man now knows the sum even though we don't. Yet he still insists that there isn't enough info. This must mean that there are two permutations with the same sum; otherwise the man could have easily deduced the ages.

The only pair of permutations with the same sum are 8 3 3 and 6 6 2, which both add up to 14 (the bar's address). Now the bartender mentions his "youngest"--telling us that there is one child who is younger than the other two. This is impossible with 8 3 3--there are two 3 year olds. Therefore the ages of the children are 6, 6, and 2.

Pedants have objected that the problem is insoluble because there could be a youngest between two three year olds (even twins are not born exactly at the same time). However, the word "age" is frequently used to denote the number of years since birth. For example, I am the same age as my wife, even though technically she is a few months older than I am. And using the word "youngest" to mean "of lesser age" is also in keeping with common parlance. So I think the solution is fine as stated.

## Visit At The Kremlin

"This," explained Colonel Nevskij to the Druggar of Bongo Ghango - chief of a large country by River Ghango - "is the Buttons Room."

"I've seen a room like this in Washington," replied the big Chief, smiling with satisfaction, "there too, you couldn't see a single button. The only ones I can see here are, uh.. hehe, the ones on your uniform, Colonel!"

"Ahah, comrade Druggar likes joking. But the buttons are here," replied the Soviet, pointing at a large panel at the end of the room, "they are behind that panel."

"A very large panel," observed the Chief, "much larger than the one at the White House: I presume there are more buttons here."

"Of course, comrade Druggar: in America, only a bunch of opportunistic capitalists has a saying in the big decisions, while here, uh, here is different: the entire Soviet community, through its representatives, takes part in the decision process of the Union."

"Any citizen could then come here and press the buttons?"

"Err, no, not exactly. If I tried to do it, the room would fill up with narcotic gas, an alarm would set off, and... Well, no need to talk about that. For each button there is a slot, into which a magnetic card must be inserted, to activate the corresponding button. Therefore, no card, no button. To launch the missiles, every button must be activated and pressed, and only a handful of comrades holds the magnetic cards, which of course, each of them has a different code from the others. The personalities holding the cards are the Secretary of the Communist Party, the President of the Praesidium, the Chief of the KGB, and five comrades, Heroes of the Soviet Union. The distribution - and here is the originality of our system - is such that the Secretary of the Party holds the complete set of codes, and so he can launch the missiles by himself; if the Secretary is not available, the missiles can be launched by the President of the Praesidium together with the Chief of the KGB, or by anyone of these two, together with any two of the five Heroes of the Union. If - Marx forbid - the Secretary, the President, and the Chief have all been victimised by an imperialistic attack, our nuclear response can be initiated by any four of the five Heroes of the Soviet Union; any four of them would be sufficient to have the entire set of magnetic cards to activate the buttons."

"So, how many buttons are there?" asked the Chief.

What is the minimum number of buttons, and how are they distributed?

### Visit At The Kremlin Puzzle Solution

There are 20 buttons. This is because there are 10 combinations of Heroes in pairs of 2, and this is multiplied by 2 because these combinations have to be mapped to two different persons (the President of the Praesidium or the Chief of KGB). The magnetic cards, as held by the eight persons, and marked with an X, are distributed as follows:
Person Buttons
Secretary of Party X X X X X X X X X X X X X X X X X X X X
President of Praesidium X X X X X X X X X X X X X X X - - - - -
Chief of KGB - - - - - X X X X X X X X X X X X X X X
1st Hero X X X X - - - - - - - X X X X X X X X -
2nd Hero X X X - X X X X - - - - - - X X X X - X
3rd Hero X X - X X - - X - X X - - X - X X - X X
4th Hero X - X X X - X - X - X - X - - X - X X X
5th Hero - X X X X X - - X X - X - - - - X X X X

## Swapping Art

"Four drawings by Max Ernst are worth as much as five sketches by Magritte, do you agree?" asked Giorgio Parconi, an Italian art dealer. He was tired of arguing over this.

"D'accord!" agreed Cesar Blanchard, who was the director of a Parisian art gallery.

"And we all agree that two sketches by Magritte plus one drawing by Ernst are worth as much as two paintings by Bacon. Right?"

"Bon," nodded the frenchman.

"So, I'm offering you four drawings by Ernst plus one sketch by Magritte, and in return you give me three sketches by Magritte and two paintings by Bacon. It's perfectly fair, isn't it?"

Blanchard remained silent, he had the feeling that something was wrong.

Was the Italian dealer offering a fair swap?

### Swapping Art Puzzle Solution

The swap is unfair. If we abbreviate with an E the drawings by Ernst, an M for Magritte's sketches, and a B for Bacon's paintings, we can rewrite the equations as stated by the Italian dealer as:
1. EEEE = MMMMM (both dealers agreed on this)
2. MME = BB (again, both dealers agreed on this too)
3. MMMBB = EEEEM (the French dealer wasn't sure of this)
Now, if for the 3rd equation we substitute BB with MME (from equation 2), we'll have a 4th equation: MMMMME = EEEEM. But the 1st equation states that MMMMM = EEEE, so it is possible to cancel out, in equation 4, MMMMM on the left and EEEE on the right. This would leave us with the equation E = M, which does not fit with equation 1, where E is obviously greater than M.

The problem gives us 3 equations:
1. 4x = 5y
2. 2y + x = 2z
3. 3y + 2z = 4x + y

Equation 2. can be rewritten as:
4. x = -2y + 2z

Equation 3. can be rewritten as:
5. 4x = 2y + 2z

Adding equations 4. and 5. gives us:
6. 5x = 4z

Combining 1. and 6., we get:
7. 4x = 5y = (16/5)z

If we convert the offer (3.) in terms of y, we get:
8. 3y + 2(25/16)y = 5y + y
ie 3y + (25/8)y = 6y
ie 6.125y = 6y

The last equation is not absolutely true, which proves the swap is unfair.

## Top Secret

With his heart rate increasing steadily, James Bents (alias Lt-Colonel Ivanovic Zdanov, as far as the KGB were concerned) lined up behind the scientists who were walking towards the internal gate. Thanks to his forged documentation, he was able to pass through the two previous gates. He was aware that to get right inside the missile launch-pad, he would need to supply a password. He had been informed that the password changed daily. Only his extreme cool and many years of training enabled him to contain the fear.

The two scientists in front of him reached the gate, which was patrolled by machine-gun wielding soldiers. He strained to hear the voices of the people ahead of him in the queue.

"Six," replied the first scientist.

The first scientist strode through the gate as the second one walked to the guard.

"Three," replied the second scientist and walked through.

Relief and confidience spread through Bents; the method that drove questions and answers was trivial. He stepped forward.