[Other] Word problems for fun!

[Jonny]

Haha, I know you were kidding... I was just being a butt.

 

[Red Herring]

Then let's move on to something that can be solved without being a Rasputin lookalike!

Three Palefaces were taken captive by a hostile Indian tribe. According to tribe’s custom they had to pass an intelligence test, or die. The chieftain showed 5 headbands – 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly – they passed the test and could go free, if not – they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few minutes of silence, the first man in the line said: "My headband is ...".
What color was his head band? Why?

 

[Red Herring]

Also:

One of twelve tennis balls is a bit lighter or heavier (you do not know which) than the others. How would you identify this odd ball if you could use an old two-pan balance scale only 3 times?
You can only balance one set of balls against another, so no reference weights and no weight measurements.

 

[Jonny]

So, I will think aloud for this solution:

If the first two men had both red headbands, then the last man would immediately guess correctly: White

Therefore, since the last man did not guess, of the two men in front, one has red and one has white OR both have white.

Then, if the second man saw red in front of him, he would guess correctly: White

Thus, after knowing that the second and third man both could not guess, the first man would know the answer to his color: White

 

[Red Herring]

yup

 

[Jonny]

Suppose there exists a country where girls are more valuable than boys. However, it is also the case that a small family size is valuable. Thus, families will continue to have babies until they have exactly 1 daughter, and then stop having children. If we assume that the survival rates for men and women are the same, and we assume that the chance of having a boy and the chance of having a girl are equal: What will the ratio of men to women be in the population?

 

[Red Herring]

It is still 50:50.

There is still a daughter born for every son. When they stop is irrelevant if you look at the whole population. Within one family you could still end up with, say, five sons and one daughter, but there are enough families with one and only one daughter to balance it.

 

[Jonny]

Correct. If we think about each birth individually, there is always a 50% chance a boy is born and a 50% chance a girl is born.

 

[Kuthtuk]

Get this one, You find yourself stranded on a lonesome road because your car broke due to a massive snow storm, you use your celphone to find that help will only come on the morning after and to make situation worst your down to your last cigarrete. As night settles you realise that spending the night inside the car would be suicide because it gets awfully cold. Thats when you spot an abandoned cabin a few meters ahead, as you enter you find a few candles, an old fire wood stove and a huge fire place. Whats the first thing you must light?

 

[esidebill]

Get this one, You find yourself stranded on a lonesome road because your car broke due to a massive snow storm, you use your celphone to find that help will only come on the morning after and to make situation worst your down to your last cigarrete. As night settles you realise that spending the night inside the car would be suicide because it gets awfully cold. Thats when you spot an abandoned cabin a few meters ahead, as you enter you find a few candles, an old fire wood stove and a huge fire place. Whats the first thing you must light?

Something to do with the cigarette perhaps. You mentioned nothing about having anything to created a light. Don't cars have cigarette lighters?

 

[Kuthtuk]

Something to do with the cigarette perhaps. You mentioned nothing about having anything to created a light. Don't cars have cigarette lighters?

Haha Yes! People create complicated lines of thought like " first the candle so I can see, then i light the fire place....." but they forget that you need a least an inicial fire to start the whole process! If you answer "But how will start the fire?" is the correct answer.

 

[fragrance]

I see a thing. Of this thing I know these three:
1) The man who makes this will sell it.
2) The man who buys this will not use it.
3) The man who uses this will not know it.

What do I see?

A coffin!

 

[fragrance]

What's the next number?

1
11
21
1211
111221
?

 

[Jonny]

What's the next number?

1
11
21
1211
111221
?

Based on our system of counting/mathematics, there isn't any pattern I can see. Why can't I see it?!?!?! There must be some trick to this... /scratches head

 

[Jonny]

Hahahahaha, got it!!! It took me writing it out and reading aloud to get it. Tricky tricky tricky...

1
11
21
1211
111221
312211
?

 

[Red Herring]

hua hua hua!

Damn it. It didn't occur to me to read it out loud, but when Jonnyboy said that and I did, I got it! Good one!

What about my tennis ball problem?

 

[Jonny]

What about my tennis ball problem?

One of twelve tennis balls is a bit lighter or heavier (you do not know which) than the others. How would you identify this odd ball if you could use an old two-pan balance scale only 3 times?
You can only balance one set of balls against another, so no reference weights and no weight measurements.

I've encountered a similar problem before, so I'll abstain. It's a good one though.

 

[Red Herring]

You have 12 coins before you in a dark room, 6 of them heads and 6 of them tails. You can not see them and have no other way (like touching, etc) to tell which is which. Your task is to divide them into two groups of 6 coins each in such a way that group A has the same number of heads and tails as group B. You are allowed to turn one or several coins as often as you like until you have the correct number of heads and tails. What is the easiest and fastest way to achieve the task?

 

[Jonny]

Reflection principle. Split them into two groups, and turn all six coins from one of the groups over.

 

[Red Herring]

Reflection principle. Split them into two groups, and turn all six coins from one of the groups over.

[YOUTUBE="http://www.youtube.com/watch?v=p9vP8DjEB6Y"]You're no fun anymore[/YOUTUBE]