Brain Teaser for ATOTrs

[Yax]

The 100 Cables (no knowledge of math required):

In a very tall building, 100 cables were placed connecting the roof to the basement. Unfortunately the people that placed them forgot to tag them, so nobody knows which end at the top leads to which end at the bottom. But, fortunately our engineers came up with a series of experiments that led to a solution. In each experiment they connected several (one or more) pairs of cables at the roof to batteries, so that each battery is connected to exactly 2 cables (one to the '+' and one to the '-'). They would then go down, and using a light bulb they would find pairs of cables that turn the light bulb on. They would mark their results (doesn't matter how), and then go up to make the next experiment. What is the minimum number of experiments that is required to know exactly which cable end at the roof leads to which cable end at the bottom? (Show how to do it, and prove that it is minimal).
Note: obviously the maximum number of pairs that can be connected in one experiment is 50, because each battery connects exactly 2 cable ends and there are 100 of these. Now imagine that the cables at the roof are R1, R2, ...R100, and that the cables at the basement are B1, B2, ...B100. If we connect cables (R1, R2) and (R3, R4) at the top, and then go down to the basement we find 2 pairs. Say that these are (B1, B2) and (B3, B4). Notice that in this case all the following assignments are valid: (R1->B1, R2->B2, R3->B3, R4->B4) (R1->B2, R2->B1, R3->B3, R4->B4) (R1->B3, R2->B4, R3->B1, R4->B2) and so on (5 more options).

 

[wbresson]

15962418966

 

[neonerd]

42

 

[Yax]

Answer is 2. Now can someone explain why?

 

[Baked]

Because you need 2 to tangle.

 

[Confused]

I would get the people who installed them back in to pull them out and run them again, because they obviously didn't do their job properly.


If I were to employ them to do the job and they did that, I would refuse to pay them.

 

[YOyoYOhowsDAjello]

Originally posted by: Yax
The 100 Cables (no knowledge of math required):

In a very tall building, 100 cables were placed connecting the roof to the basement. Unfortunately the people that placed them forgot to tag them, so nobody knows which end at the top leads to which end at the bottom. But, fortunately our engineers came up with a series of experiments that led to a solution. In each experiment they connected several (one or more) pairs of cables at the roof to batteries, so that each battery is connected to exactly 2 cables (one to the '+' and one to the '-'). They would then go down, and using a light bulb they would find pairs of cables that turn the light bulb on. They would mark their results (doesn't matter how), and then go up to make the next experiment. What is the minimum number of experiments that is required to know exactly which cable end at the roof leads to which cable end at the bottom? (Show how to do it, and prove that it is minimal).
Note: obviously the maximum number of pairs that can be connected in one experiment is 50, because each battery connects exactly 2 cable ends and there are 100 of these. Now imagine that the cables at the roof are R1, R2, ...R100, and that the cables at the basement are B1, B2, ...B100. If we connect cables (R1, R2) and (R3, R4) at the top, and then go down to the basement we find 2 pairs. Say that these are (B1, B2) and (B3, B4). Notice that in this case all the following assignments are valid: (R1->B1, R2->B2, R3->B3, R4->B4) (R1->B2, R2->B1, R3->B3, R4->B4) (R1->B3, R2->B4, R3->B1, R4->B2) and so on (5 more options).

#1 your formatting hurts my eyes

#2 I'm lazy

#3... ok, i'll think about it

 

[YOyoYOhowsDAjello]

I think the answer is 6. (and I'm serious)

EDIT: let me try to write an explanation (It's not going to be proof thought)

EDIT #2: oops, I thought it was 50 cables, my new answer = 7

 

[YOyoYOhowsDAjello]

ok, you have 100 to start with...

Hook up R1 - R50 to + and R51 - R100 to -

Go down and mark all the ones that are positive and the ones that are negative (you can tell this by what part of the lightbulb you connect it to I'm assuming)

Now you have the group divided into 2 groups of cables that match each other.

Then you divide the 50 into two groups of 25 and hook up positive and negative. You can mark these differently this time.

You keep splitting them up like this and it takes 7 times to get it down to single ones.

I have no idea how you're getting 2.

 

[b0mbrman]

I can see how the answer would be 7...I can't see how the answer would be 2...

 

[Yax]

Originally posted by: YOyoYOhowsDAjello
ok, you have 100 to start with...

Hook up R1 - R50 to + and R51 - R100 to -

Go down and mark all the ones that are positive and the ones that are negative (you can tell this by what part of the lightbulb you connect it to I'm assuming)

Now you have the group divided into 2 groups of cables that match each other.

Then you divide the 50 into two groups of 25 and hook up positive and negative. You can mark these differently this time.

You keep splitting them up like this and it takes 7 times to get it down to single ones.

I have no idea how you're getting 2.

Sounds interesting. Lots of people got 7 too I think, but that's wrong. But going along with your logic, since you can have 50 + and 50 -, why not divide it 3 ways instead of 2? You can have some +, some - and some nocharge. Would that help you?

 

[YOyoYOhowsDAjello]

Originally posted by: Yax

Originally posted by: YOyoYOhowsDAjello
ok, you have 100 to start with...

Hook up R1 - R50 to + and R51 - R100 to -

Go down and mark all the ones that are positive and the ones that are negative (you can tell this by what part of the lightbulb you connect it to I'm assuming)

Now you have the group divided into 2 groups of cables that match each other.

Then you divide the 50 into two groups of 25 and hook up positive and negative. You can mark these differently this time.

You keep splitting them up like this and it takes 7 times to get it down to single ones.

I have no idea how you're getting 2.

Sounds interesting. Lots of people got 7 too I think, but that's wrong. But going along with your logic, since you can have 50 + and 50 -, why not divide it 3 ways instead of 2? You can have some +, some - and some nocharge. Would that help you?

Yeah, that's a good idea. It's still not going to bring it down to 2 though

 

[YOyoYOhowsDAjello]

I think you get down to 5 tests if you split it 3 ways all the way through

 

[TuxDave]

Originally posted by: YOyoYOhowsDAjello
I think you get down to 5 tests if you split it 3 ways all the way through

I'm not sure if your solution works. You say you keep dividing the groups into two, but what you do to one group, you have to repeat for another group so eventually you end up with a lot of experiments. But I think you're on the right track...

 

[Yax]

Originally posted by: YOyoYOhowsDAjello
I think you get down to 5 tests if you split it 3 ways all the way through

Okay, so the question is, how many ways do you have to split it to get it down to 2?

 

[shuan24]

the answer is 2.

Heres the solution/key: You never stated in the problem that all batteries were the same. So, what you do is use different batteries at different voltages (50 different voltages) and 50 different lightbulbs.

After the first step you will have R1 and R2 matching to B1 and B2 (goes up to R49 and R50 matching to B49 and B50). Now the second step is to figure out which roof cable matches to which basement cable. All you need to do now is to flip the battery around.

Third step: profit!

 

[walla]

Originally posted by: Yax

Originally posted by: YOyoYOhowsDAjello
I think you get down to 5 tests if you split it 3 ways all the way through

Okay, so the question is, how many ways do you have to split it to get it down to 2?

Well...

log base x of 50 = 2

solve for x...you get 7.07...so you would need 8 voltage levels at least. But the problem then becomes judging voltage level based on bulb brigtness. If that were possible...then that solves the problem.

Of course, why not just use a multimeter instead of a light bulb?

 

[aplefka]

Was this given in a math class?

 

[YOyoYOhowsDAjello]

Originally posted by: shuan24
the answer is 2.

Heres the solution/key: You never stated in the problem that all batteries were the same. So, what you do is use different batteries at different voltages (50 different voltages) and 50 different lightbulbs.

After the first step you will have R1 and R2 matching to B1 and B2 (goes up to R49 and R50 matching to B49 and B50). Now the second step is to figure out which roof cable matches to which basement cable. All you need to do now is to flip the battery around.

Third step: profit!

lol ok.

That seems like something an engineer would do... go out and buy 50 different batteries of different voltages to check the bulbs instead of walking up a few flights of stairs 5 times.

 

[BudAshes]

Originally posted by: Baked
Because you need 2 to tangle.

lmfao

 

[shuan24]

why walk 5 times when you can cut it down to 2?

 

[YOyoYOhowsDAjello]

Originally posted by: shuan24
why walk 5 times when you can cut it down to 2?

I already said: so you don't have to buy 50 special batteries for testing purposes

If budget is unlimited, make one trip downstairs in the process of wiring it all over again but correctly this time.

 

[YOyoYOhowsDAjello]

Oh, I thought of a better answer.

The question says "our engineers"

So, instead of buying 50 batteries with different voltages, get them some walkie talkies. 1 engineer @ the top, 1 @ the bottom.

The question seems to define an experiment as a session of being upstairs and then downstairs.

By this definition, 1 engineer staying on top and doing intividual wire pairs coordinating with the other would all be one experiment.

So, the answer is 1.

 

[Goosemaster]

Originally posted by: Xafgoat

Originally posted by: Baked
Because you need 2 to tangle.

lmfao

 

[Trevelyan]

Originally posted by: Xafgoat

Originally posted by: Baked
Because you need 2 to tangle.

lmfao

haha thats the answer right?