Logic problems

[AnnaMall]

This occured to me when pineaple popped into chat and posted a math problem to solve and all went *getting some paper*

Problem #1: You are on the ground floor with 3 light switches. Those light switches light bulbs on the first floor. You need to match which switch turns on which bulb by going up the stairs just once.

Spoiler for Hidden:

Its a logic problem.... the answer is not something like, look up the stairs and see the bulbs. There is a perfectly doable logical explanation for doing this.

Problem #2: You are staying in a hotel and you got no money to pay rent. You have a golden chain with 7 rings. The owner agreed to get payed by the chain at a rate of 1 ring a day. You want to stay there for a week, go home get the money and pay in order to get back the chain. Problem is that you have to give the hotel owner a ring every day BUT you dont want to destroy the chain by cutting each ring. What is the minimum cuts that needs to be done?

Spoiler for Hidden:

Again its not a trick question... owner must have at day 3 three rings, day 6 six rings etc

In order to not spoil it for everyone I can pm you the answers. Would love it if you flexed your brain a bit before asking for the answers though

[Pineapple]

Answers in spoilers.

This occured to me when pineaple popped into chat and posted a math problem to solve and all went *getting some paper*

Problem #1: You are on the ground floor with 3 light switches. Those light switches light bulbs on the first floor. You need to match which switch turns on which bulb by going up the stairs just once.

Spoiler for Hidden:

Its a logic problem.... the answer is not something like, look up the stairs and see the bulbs. There is a perfectly doable logical explanation for doing this.
I believe the answer was something convoluted, along the lines of "After you can be sure that the light bulbs have been turned off for 30 seconds, flip switch A, wait 30min so light bulb A heats up, flip switch B, run to the 2 on and 1 off light bulbs; lit and hot is light bulb A, lit and cold is light bulb B, off is C." Otherwise, flip switch A again so that the 3 light bulbs are distinguished by off/hot, on, off/cold.

Problem #2: You are staying in a hotel and you got no money to pay rent. You have a golden chain with 7 rings. The owner agreed to get payed by the chain at a rate of 1 ring a day. You want to stay there for a week, go home get the money and pay in order to get back the chain. Problem is that you have to give the hotel owner a ring every day BUT you dont want to destroy the chain by cutting each ring. What is the minimum cuts that needs to be done?

Spoiler for Hidden:

Again its not a trick question... owner must have at day 3 three rings, day 6 six rings etc
Not a trick question? So not 1 time, so you can take the rings off the chain and give them to the owner one-by-one?
Oh, that type of chain (made up WITH rings). Assuming trading, twice into parts of 1, 2, and 4 ... 1 = 1, 2 = 2, 3 = 1 + 2, 4 = 4, 5 = 4 + 1, 6 = 4 + 2, 7 = the whole thing.
...But the only way to cut a chain made up of rings is to cut a ring so that it becomes either half of a ring or it loses its "ring-ness', right?

In order to not spoil it for everyone I can pm you the answers. Would love it if you flexed your brain a bit before asking for the answers though

[Absol]

I've been thinking what Pineapple said for first question, but was unsure of it.

For second question,

Spoiler for answer:

cut it into three parts, 1-2-4.
Day 1: 1 ring
Day 2: trade 1 ring to the 2 rings
Day 3: give the 1 ring
Day 4: trade all for 4 rings
Day 5: repeat from day 1

[dracomageat]

1st question:

Spoiler for Hidden:

Turn on 2 lights. After some time, turn off one of them. One of the off bulbs should be warm.
It's very simple when you know the answer.

2nd:

Spoiler for Hidden:

Interestingly, 2 cuts can also give 1,1,3,2, though that isn't really relevant.

[Kakerlake]

2nd: I like pretty pictures. That's probably the fewes cuts one can make.

Spoiler for Pretty Picture:

But seriously, just give the whole chain to the dude, stay your week and keep the chain whole without cutting -.-

[AnnaMall]

2nd: I like pretty pictures. That's probably the fewes cuts one can make.

Spoiler for Pretty Picture:

But seriously, just give the whole chain to the dude, stay your week and keep the chain whole without cutting -.-

Its about how many rings you destroy, not how many cutting actions you perform.

Would appreciate if someone through some problem for my brain too, jealous of brain tingling

[Kakerlake]

Its about how many rings you destroy, not how many cutting actions you perform.

Would appreciate if someone through some problem for my brain too, jealous of brain tingling

Aw^^ well, in that case, the solution of Absol seems muchos legitos.

2 random (and quite old) riddles that just popped up in my head are these:
(no trick questions, they have very logic answers)

1:
You are on a small island far away from any civilisation and are baking a cake in your oven. To make it the perfect cake, it has to be heated for exactly 45 minutes. One second more or less and it'll explode or something.
All you have are 2 match cords, which each burn exactly 1 hour, but not consistantly as you've hand made them yourself. (so cutting the cord in half won't give you half an hour buring time, but yes, each one burns exactly 1 hour).
Also, you have a bunch of matches and a match box on your island.
How can you say when 45 minutes passed, with the aid of the two match cords?

2:
Evil aliens have kidnapped you and 3 of your buddies. Because they are so evil (and slightly stupid) they want to play a game.
All 4 of you are burried with only your head above the ground, alligned so that person A and B don't see anyone, person C sees only person B and person D sees C and B.
(looks something like this: <O O> O> O> )
There are 2 red and 2 blue hats, each one of you has one hat, but you can't see your own hat.
If anyone sais what hat he has, everyone is free to go, one false answer and... well, let's just say you don't want to answer falsly.
Which of you folks gives the correct answer?

[The_Mormegil]

The one about the lights is interesting... it's the only one I can't solve right away. (Although I did know the one about the matches and strings already...).

[Thalas]

Its about how many rings you destroy, not how many cutting actions you perform.

Would appreciate if someone through some problem for my brain too, jealous of brain tingling

Aw^^ well, in that case, the solution of Absol seems muchos legitos.

2 random (and quite old) riddles that just popped up in my head are these:
(no trick questions, they have very logic answers)

1:
You are on a small island far away from any civilisation and are baking a cake in your oven. To make it the perfect cake, it has to be heated for exactly 45 minutes. One second more or less and it'll explode or something.
All you have are 2 match cords, which each burn exactly 1 hour, but not consistantly as you've hand made them yourself. (so cutting the cord in half won't give you half an hour buring time, but yes, each one burns exactly 1 hour).
Also, you have a bunch of matches and a match box on your island.
How can you say when 45 minutes passed, with the aid of the two match cords

Spoiler for Hidden:

Take first match cord and light it on the both ends, this way you get 30 minutes. Take the second match cord and ligth it at the both ends and the middle, this way you get 15 Minutes. Now's you rare Super delicate chocolate cake baked, so now it leaves you with annoying question: How do I get home?

2:
Evil aliens have kidnapped you and 3 of your buddies. Because they are so evil (and slightly stupid) they want to play a game.
All 4 of you are burried with only your head above the ground, alligned so that person A and B don't see anyone, person C sees only person B and person D sees C and B.
(looks something like this: <O O> O> O> )
There are 2 red and 2 blue hats, each one of you has one hat, but you can't see your own hat.
If anyone sais what hat he has, everyone is free to go, one false answer and... well, let's just say you don't want to answer falsly.
Which of you folks gives the correct answer?

Spoiler for Hidden:

B can't answer because he doesn't see anything. C cannot answer because he sees only B's head which is red or blue.
             D - He sees B's and C's hat, if their hats are of the same color, then D says just opposite color.

                                      ⇩
             But if their hats are of the different colors then D can't answer.
             C - "If D can't answer then that means that B's and C's hats are of different color" Thinks C and thinks more "So I should say the
            opposite color of the B's hat, because
            we have different hats, because D can't answer, because if we had the same hats D would answer.

[Kakerlake]

Spoiler for Hidden:

Take first match cord and light it on the both ends, this way you get 30 minutes. Take the second match cord and ligth it at the both ends and the middle, this way you get 15 Minutes. Now's you rare Super delicate chocolate cake baked, so now it leaves you with annoying question: How do I get home?

Sadly, this doesn't work, because:

All you have are 2 match cords, which each burn exactly 1 hour, but not consistantly as you've hand made them yourself. (so cutting the cord in half won't give you half an hour buring time, but yes, each one burns exactly 1 hour).

So, your second cord just burned up on one side after 10 minutes and on the other side after 20 minutes. Sry, your cake exploded

[drolly]

May I add a riddle? It's a variation of Kakerlake's second one but I suggest that you only open the spoiler if you like mathematics. Well, it's too nice not to be posted here.

Spoiler for riddle:

Infinitely many dwarfs are kidnapped by the devil and thrown in hell. He offers them a deal. Tomorrow he'll put a hat on each dwarf's head, such that everyone can see every hat but their own one. The hats are either black or white. They won't be allowed to communicate after that and every action to find out the colour of one's own hat is illegal (taking it down, looking into a mirror etc.). However, they can talk during the night before the game begins (and believe me, dwarfs talk much and fast).

The devil will then ask each dwarf about the colour of their hat (in a private conversation). If only finitely many dwarves make a wrong guess, they'll all come free. How do they escape?

Spoiler for mathematicians:

Yes, you may assume the Axiom of Choice.

And don't let this keep you from finding a correct answer to Kakerlake's first riddle

Edit: replaced "dwarves" by "dwarf" (interesting how Tolkien popularized the use of the "incorrect" plural), closed an obvious loophole.

[Laxadarap]

Ok, time for my old riddles, both are pretty easy.

Your driving and your car breaks down outside of an abandoned house.  You enter, looking for help and try and switch the light, but the powers out.  You wander through the darkness and walk through a door.  The door swings shut and locks behind you, with three doors in front of you.  Each one says, "Enter this door and you will be killed by...".  First door says electric chair, second door says firing squad, third door says poison gas.  Which door do you choose, and why?



You are scheduled to be executed.  You can either be humiliated publically with a hanging, after your limbs are chopped off, tossed into a pit full of lions that haven't eaten a 3 months, or tarred and feathered, then lit on fire.  Which do you choose?