Logic puzzle corner

[Amarillo]

Use this thread to post your logic puzzle problems.


The four box problem.

Two unrelated people walk into a VW van centre to be greeted by the chief executive of VW(UK).

“Congratulations”, says he. “One of you is our millionth customer, but we don’t know who… We have for our millionth customer a brand new California, with options of your choice, but now we don’t know who to give it to.”

“To resolve this, we propose a double or quits challenge. Should you succeed you will both drive away in a California, but should you fail all we can present you with is a Van Centre key ring (without the key).”

“Shortly I will take one of you into a room with four boxes numbered 1, 2, 3 & 4. You will see me place two key rings in each box, only one of the boxes will have keys on the key ring. I will then close all four boxes, and place a coin on the top of each box, each coin either showing a heads or a tails. You will then be able to reverse just one coin if you want to.”

“You will then be taken to another room, and the other person will be led into the room and given the opportunity to open just one box for a prize of a key ring each or a California each.”

“You may now confer”.

What strategy can the two customers agree to ensure they win a California each?

 

[The Tall Luthier]

The only solution I can think of is to choose the overturned coin from one good box and place it onto the coin of the other good box. Doesn’t sound within the rules though

 

[Amarillo]

The only solution I can think of is to choose the overturned coin from one good box and place it onto the coin of the other good box. Doesn’t sound within the rules though

The solution is neat elegant, and once know, obvious.

Your solution is incorrect.

 

[andyinluton]

I will just say 1,2,3,4 HHH&TTT, HHT&TTH, HTH&THT, THH&HTT


Enough of an answer Amarillo ?

 

[flymartin]

I will just say 1,2,3,4 HHH&TTT, HHT&TTH, HTH&THT, THH&HTT


Enough of an answer Amarillo ?

Well done. I got stuck trying to work out how to use binary..

 

[Mollymoo]

Use this thread to post your logic puzzle problems.


The four box problem.

Two unrelated people walk into a VW van centre to be greeted by the chief executive of VW(UK).

“Congratulations”, says he. “One of you is our millionth customer, but we don’t know who… We have for our millionth customer a brand new California, with options of your choice, but now we don’t know who to give it to.”

“To resolve this, we propose a double or quits challenge. Should you succeed you will both drive away in a California, but should you fail all we can present you with is a Van Centre key ring (without the key).”

“Shortly I will take one of you into a room with four boxes numbered 1, 2, 3 & 4. You will see me place two key rings in each box, only one of the boxes will have keys on the key ring. I will then close all four boxes, and place a coin on the top of each box, each coin either showing a heads or a tails. You will then be able to reverse just one coin if you want to.”

“You will then be taken to another room, and the other person will be led into the room and given the opportunity to open just one box for a prize of a key ring each or a California each.”

“You may now confer”.

What strategy can the two customers agree to ensure they win a California each?

Use this thread to post your logic puzzle problems.


The four box problem.

Two unrelated people walk into a VW van centre to be greeted by the chief executive of VW(UK).

“Congratulations”, says he. “One of you is our millionth customer, but we don’t know who… We have for our millionth customer a brand new California, with options of your choice, but now we don’t know who to give it to.”

“To resolve this, we propose a double or quits challenge. Should you succeed you will both drive away in a California, but should you fail all we can present you with is a Van Centre key ring (without the key).”

“Shortly I will take one of you into a room with four boxes numbered 1, 2, 3 & 4. You will see me place two key rings in each box, only one of the boxes will have keys on the key ring. I will then close all four boxes, and place a coin on the top of each box, each coin either showing a heads or a tails. You will then be able to reverse just one coin if you want to.”

“You will then be taken to another room, and the other person will be led into the room and given the opportunity to open just one box for a prize of a key ring each or a California each.”

“You may now confer”.

What strategy can the two customers agree to ensure they win a California each?

Tell the other customer which number box the keys are in as you saw the keys being put into the box.

Alternatively shake the boxes

 

[Amarillo]

I will just say 1,2,3,4 HHH&TTT, HHT&TTH, HTH&THT, THH&HTT


Enough of an answer Amarillo ?

Yes - perfect and correct.

Full explanation for anyone who doesn’t understand your solution.

The two customers work out that they only need consider three of the four coins. Those on boxes 1, 2 & 3 are the obvious ones to use for the “message” from Customer A to Customer B.

Those three coins could originally be in 1 of 8 possible combinations, and those combinations can be split into four pairs, one pair as a “message” for each box, as suggested by Andy:
Box 1 {HHH or TTT}
Box 2 {HHT or TTH}
Box 3 {HTH or THT}
Box 4 {HTT or THH}

Whatever combination the coins began with, one or other of the above pairs can be made by flipping over one of the three coins.

But if the keys are in a box already indicated by the lay of the coins, and a coin MUST be flipped (I didn’t specify this in the original problem) the forth coin could be flipped and the “message” left unchanged.

 

[WelshGas]

Turn around, straight to the nearest Mercedes Dealer. Buy a Marco Polo, which comes with the the same un- knowledgeable Dealership staff, dreadful Customer Service and the bonus of a failing roof, but costs a little less than a California.

 

[Amarillo]

Trapped Californias

There is a gentle hill, where by some freak it takes exactly the same amount of fuel for a California to drive up, as it does for the same California to drive down towing a smaller California.

Caddy California 11 Litre of fuel
California Beach 12 Litres of fuel
-Towing a Caddy downhill 12L
Grand California 600 14L of fuel
-Towing Caddy downhill 14L
-Towing Beach downhill 14L
Grand California 680 15L of fuel
-Towing Caddy downhill 15L
-Towing Beach downhill 15L
-Towing GC 600 downhill 15L

Smaller Californias cannot tow larger Californias. Neither can any California tow more than one other California; they have just one indivisible tow rope and wouldn’t break the law even if they had two.

The four Californias: Caddy, Beach, Grand 600 and Grand 680 meet at the summit of this freakish hill, and the drivers go off for a walk. When they return to their vehicles the drivers of the Caddy, 600 and 680 discover their fuel tanks have been drained by a thief. The Beach owner (who is a clever chap) finds his tank has not been tampered with, and he has exactly 62 litres of fuel remaining.

The four drivers find a way to siphon all the remaining fuel from one tank to another (without loss) but cannot find a way to siphon just part of a tank.

Without trickery or magic, how can all four Californias escape the freaky hill?

 

[larrylamb]

F*%k me Tom, I'm trying to work

 

[andyinluton]

Without trickery or magic, how can all four Californias escape the freaky hill?

Just let off the handbrake.

 

[Amarillo]

Just let off the handbrake.

The hill is:
A. Not sufficiently steep.
B. Undulates.
C. Freakish in the way nothing like that will work.

 

[California_Ocean]

Beach tows Caddy down .... remaining 50 liters transfered to Caddy
Caddy drives up and transfers remaining 39 liters to 680
680 tows 600 down and transfers remaining 24 liters to Beach
Beach drives up (12l) and tows Caddy down (12l)

All fuel gone, all Californias at the bottom.

 

[Amarillo]

Beach tows Caddy down .... remaining 50 liters transfered to Caddy
Caddy drives up and transfers remaining 39 liters to 680
680 tows 600 down and transfers remaining 24 liters to Beach
Beach drives up (12l) and tows Caddy down (12l)

All fuel gone, all Californias at the bottom.

Perfect - great explanation.

 

[Ch1pbutty]

All fuel gone, all Californias at the bottom.

So no one gets home. Strange logic.

 

[Amarillo]

So no one gets home. Strange logic.

How do you know that home isn’t at the bottom of the hill?

 

[andyinluton]

Why didn't they just call VW assist?

 

[Amarillo]

Why didn't they just call VW assist?

No mobile signal.

 

[yossarian]

More generally the problem could be stated:

Encode the numbers 1 to 4 by optionally flipping one bit of 3 random bits.

I found the language more challenging than the encoding.

Some might find this clearer:

Initial
	Encode 1	Encode 2	Encode 3	Encode 4
000	000	001	010	100
001	000	001	101	011
010	000	110	010	011
011	111	001	010	011
100	000	110	101	100
101	111	001	101	100
110	111	110	010	100
111	111	110	101	011

 

[andyinluton]

More generally the problem could be stated:

Encode the numbers 1 to 4 by optionally flipping one bit of 3 random bits.

I found the language more challenging than the encoding.

Some might find this clearer:

Initial
	Encode 1	Encode 2	Encode 3	Encode 4
000	000	001	010	100
001	000	001	101	011
010	000	110	010	011
011	111	001	010	011
100	000	110	101	100
101	111	001	101	100
110	111	110	010	100
111	111	110	101	011

Is that an answer or a new problem?

 

[yossarian]

Is that an answer or a new problem?

It's the original problem restated. I didn't really understand the original because I thought there was only two coins involved. I only figured it our once I saw the solution.

 

[Amarillo]

It's the original problem restated. I didn't really understand the original because I thought there was only two coins involved. I only figured it our once I saw the solution.

Restating the logic problem as you suggest changes it from a logic problem to a maths problem.

Most of the effort in solving logic problems is converting the story to an equation or similar.

 

[The Tall Luthier]

Another problem @Amarillo if you don’t mind.

Three garage doors, there’s a two tone Ocean behind one of them, the others are empty.

You have two chances to guess the right door.

After your first guess, say door one, the dealer will raise a different door that they know is an empty garage. One of doors two or three must be empty.

You then get to change your mind, if you want to. Should you?

The answer is yes you should, but why?

 

[California_Ocean]

Another problem @Amarillo if you don’t mind.

Three garage doors, there’s a two tone Ocean behind one of them, the others are empty.

You have two chances to guess the right door.

After your first guess, say door one, the dealer will raise a different door that they know is an empty garage. One of doors two or three must be empty.

You then get to change your mind, if you want to. Should you?

The answer is yes you should, but why?

That's the Monty Hall Problem ....

Monty Hall Problem: Solution Explained Simply

How to solve the puzzle in easy steps! The Monty Hall problem is a probability puzzle named after the original host of the TV show Let's Make a Deal.

www.statisticshowto.com

The problem was explained by Marilyn vos Savant in 1990 (an extremely clever person) and caused a huge furor at the time.

Marilyn vos Savant - Wikipedia

en.wikipedia.org

 

[California_Ocean]

You have to drive 12km in your California.

You drive the first 6km at an average speed of 30km/h.

How fast do you need to drive the remaining 6 km to achieve an average speed of 60km/h for the whole journey?