Thread: aelan's weird and random tests

1. How do you do those hiding content tags again? x-X Or are they even implemented?

I've heard of some of them... maybe I'm cheating?

1. Is there more lemonade in the orange juice or more orange juice in the lemonade? - more orange in lemon? I don't want to overthink... how much orange did you remove when taking a spoonful of lemon?

2. You have three boxes of fruit. - take one from the "apples" box... if you get an apple, then it's the mix box... if it's an orange, then it's oranges OR the mix box. If you take one from the mix box... then you know for sure that one is apple or orange. ERROR x-X A box labelled incorrectly as apples can be a mix box or the orange box...

I have a solution! Don't look at the piece of fruit at all! Stick your hand in all three boxes and feel for the shape. Don't take any out or look. DONE! ^^;;;

3. At a family reunion - skipped, headache lol I'll go back and try later I promise

4. You have two slow-burning fuses - Why is this one easier than #3? Lit one fuse normally... at the same time lit both ends of the other fuse. When the fuse with 2 ends finished burning (1/2 hr), lit the other end of the normally lit fuse (now "1/2" finished). When that is finished... it'll be 45 minutes.

7. You have ten boxes, each of which contains nine balls. The balls in one box each weigh 0.9 pounds; the balls in all the other boxes weigh exactly one pound each. You have an accurate scale in front of you, with which you can determine the exact weight, in pounds, of any given set of balls. How can you determine which of the ten boxes contains the lighter balls with only one weighing? -
Steps:
1. label all boxes from 1 - 10
2. take 1 ball from box 1, 2 balls from box 2, 3 from 3... up to 9 from box 9
3. stuck all of them on the scale and weigh.
4. 45 Pd = box 10 is lighter, 44.9 Pd = box 1 is lighter, 44.8 Pd = box 2, 44.7 Pd = box 3... 44.1 Pd = box 9

The rest I need to think so more on... I feel like giving answers that will work but isn't the "correct" one at all. *smacks head*

2. Originally Posted by nightning
2. You have three boxes of fruit. - take one from the "apples" box... if you get an apple, then it's the mix box... if it's an orange, then it's oranges OR the mix box. If you take one from the mix box... then you know for sure that one is apple or orange. ERROR x-X A box labelled incorrectly as apples can be a mix box or the orange box...
It's more like;

Take from mixed: whatever is inside is what the box is (it can't contain mixed fruits because the label is wrong). Then you exchange the "wrong" label from the box with a lable and add the mixed label to that box.

ie:

Box a = "Mixed fruit" = wrong. Box a contains Apples.
Box b = label is apple(or orange), so take off label and give to box a.
Box c = label is wrong, so take it off and... only box it can go on is box b (box a is now correct). So box b gets box c's label and box c gets box a's label

3. family reunion-

7 people- a older couple, thier son and daughter in law and their kids, one daughter and 2 sons!

4. Originally Posted by ptgatsby
It's more like;
Ah! *nods head* Yes yes... I see now...

5. pt: correct *star!*

nightning:
OJ question, assume when you stir in the OJ into the lemonade, you get an evenly mixed solution. If you draw it out it is easier.

I lol-ed at your molesting the fruits solution. That's a different form of lateral thinking!

*star* to the balls question.

The fuse question takes a bit of out of the box thinking, it is why I put it as slightly more difficult. There's no way to solve it unless a person realises what you realised.

whatever, the identity of 3 of your people are wrong, but you've got the right number.

6. Originally Posted by aelan
The fuse question takes a bit of out of the box thinking, it is why I put it as slightly more difficult. There's no way to solve it unless a person realises what you realised.
I found the hat problem the hardest (I needed to visualise it by writing it down, then it was ok)...

The fuse one irritated me because uneven timing means there is no "real" solution possible, even as given. Meh.

7. Originally Posted by aelan
whatever, the identity of 3 of your people are wrong, but you've got the right number.
I wasn't looking at the question while typing the answer- I guess I got a bit mixed up!

8. Originally Posted by ptgatsby
I found the hat problem the hardest (I needed to visualise it by writing it down, then it was ok)...

The fuse one irritated me because uneven timing means there is no "real" solution possible, even as given. Meh.
You've solved all?!

The one that irritated me the most was the Monty Hall paradox actually. I get the answer, but I can't accept it *lol*. There's a certain dissonance I cannot explain.

Originally Posted by whatever
I wasn't looking at the question while typing the answer- I guess I got a bit mixed up!
Please tell me you won't take a wrong child home too.

9. Originally Posted by aelan
You've solved all?!

The one that irritated me the most was the Monty Hall paradox actually. I get the answer, but I can't accept it *lol*. There's a certain dissonance I cannot explain.
Yup, but mind you I've seen most of them before in some form or another.

There was a talk about monty hall on another thread here - http://www.typologycentral.com/forum...html#post51855 was the post I have saved (because of attachments), but isn't dealing with the problem itself - it's back and forth between a few different problems.

If I had more time, I would of done those other (and very difficult... ) problems too, since I haven't seen all of those already.

10. Without looking at anyone else's answers:

Originally Posted by aelan
1. You have two cups, one containing orange juice and one containing and equal amount of lemonade. One teaspoon of the orange juice is taken and mixed with the lemonade. Then a teaspoon of this mixture is mixed back into the orange juice. Is there more lemonade in the orange juice or more orange juice in the lemonade?
There's more orange juice in the lemonade, because the teaspoon put into the orange juice was not purely lemonade, so there would be (slightly) less of it than if it was pure.

Originally Posted by aelan
2. You have three boxes of fruit. One contains just apples, one contains just oranges, and one contains a mixture of both. Each box is labeled - one says "apples," one says "oranges," and one says "apples and oranges." However, it is known that none of the boxes are labeled correctly. How can you label the boxes correctly if you are only allowed to take and look at just one piece of fruit from just one of the boxes?

Well, taking a look at one piece of fruit from each box would give you one of one type of fruit, and two of the other type. Say, to make it easier to explain, I'll say we pull out two apples and one orange.

So clearly the orange came from the orange box. So one of the other boxes is labeled 'orange'. The third box (from which we pulled out an apple and is not labeled 'orange') we know also to have the wrong label, so logically there's only one choice left: the correct label for the third box is the one that the box containing only oranges sports. Then naturally the label that was on this third box is really the one for the one originally with the 'orange' label.

Hah, that's kinda hard to explain without specifics.

Originally Posted by aelan
3. At a family reunion were the following people: one grandfather, one grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one father-in-law, one mother-in-law, and one daughter-in-law. But not as many people attended as it sounds. How many were there, and who were they?
There are seven people: A grandfather (who is also a father and father-in-law), a grandmother (who is also a mother and mother-in-law), their son (who is also a father and a child), his wife (who is also a mother and daughter-in-law), and their three children, (who are also three grandchildren: two daughters and one son, who are also two sisters and one brother).

Originally Posted by aelan
4. You have two slow-burning fuses, each of which will burn up in exactly one hour. They are not necessarily of the same length and width as each other, nor even necessarily of uniform width, so you can't measure a half hour by noting when one fuse is half burned. Using these two fuses, how can you measure 45 minutes?

Oh, I've been asked this one before:

Initially, you light three ends of the two fuses: one on both ends and the other on just one end. When the first fuse burns out (the two burning ends having met in the middle), light the second fuse on the unlit end. When the second two burning ends meet each other, it's been half of half an hour later: i.e. 45 minutes.

Originally Posted by aelan
5. Three men, members of a safari, are captured by cannibals in the jungle. The men are given one chance to escape with their lives. The men are lined up and bound to stakes such that one man can see the backs of the other two, the middle man can see the back of the front man, and the front man can't see anybody. The men are shown five hats, three of which are black and two of which are white. Then the men are blindfolded, and one of the five hats is placed on each man's head. The remaining two hats are hidden away. The blindfolds are removed. The men are told that if just one of the men can guess what hat he's wearing, they may all go free. Time passes. Finally, the front man, who can't see anyone, correctly guesses the color of his hat. What color was it, and how did he guess correctly?
Again, I think I've heard this one before, but unfortunately this time I don't remember the answer right off. ^^

Well, if the two front men were wearing white hats, the man in the back would obviously be able to guess straight away he was wearing a black hat, and thus the other two would realise from the immediacy of his answer that they were both wearing white hats.

Hrm. Beyond that... Lol. No idea.

Originally Posted by aelan
6. Of three men, one always tells the truth, one always tells lies, and one answers "yes" or "no" randomly. Each man knows which one each of the others are. You may ask three yes/no questions, each of which may only be answered by one of the three men, after which you must be able to identify which man is which. How can you do it?

The questions you would have to ask would be something along the lines of "Will the second man say yes if I ask him if you're a liar?" or something like that.

Naturally the man that says yes or no randomly tends to throw things awry. Cause then neither of the other two could answer that question honestly. ^^

Lol. I know working out something like that would take forever with trial and error, so I can never be bothered.

Originally Posted by aelan
7. You have ten boxes, each of which contains nine balls. The balls in one box each weigh 0.9 pounds; the balls in all the other boxes weigh exactly one pound each. You have an accurate scale in front of you, with which you can determine the exact weight, in pounds, of any given set of balls. How can you determine which of the ten boxes contains the lighter balls with only one weighing?

So you're only allowed to weigh one box once? I would remove all the balls from one box, then place one ball from the second box, two balls from the third box, three balls from the fourth box and so on.

Then the weight of the box would give you your answer: if it's an even number of pounds the first box was the one with the 0.9 pound balls, if the weight is xx.9, then it was the second box, xx.8 is the third box, xx.7 the fourth, etc.

I'm assuming that the box can fit all those balls and the box's weight is negligible?

Originally Posted by aelan
8. You are on a game show. You are shown three closed doors. A prize is hidden behind one, and the game show host knows where it is. You are asked to select a door. You do. Before you open it, the host opens one of the other doors, showing that it is empty, then asks you if you'd like to change your guess. Should you, should you not, or doesn't it matter?

Oh, there's some statistical answer to this, isn't there? Even though it seems like it wouldn't matter...

Yes, I'm not going to bother figuring it out. I wouldn't know where to begin, either.

So that's 5/8! Not too bad. ^^

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