# Brain Teasers Q&A Game

1. Jan 10, 2007

### Hootenanny

Staff Emeritus
The aim of the game is simple (similar to the Math Q&A game). I will post a brain teaser, the first person to give the correct answer gets to set the next question, the first person to then answer this question correctly gets to set the following question... ad infinitum. A few rules before we begin;

1. The person who sets the brain teaser has the final and only decision as to who answered the question correctly.
2. No new question may be posted until the person who set the current question has indicated who has answered the question correctly first.
3. The person who was identified as answering the brain teaser correctly, by the person who set the current question, may then post one of their own brain teasers.
4. Each answer must be accompanied by an explanation. Any answer, correct or otherwise, which is not qualified with an explanation shall be disqualified.
5. The person whom set the question may at his/her discretion post the solution to the brain teaser which he/she has set and nominate another person to set the next question.

Let the games begin ....

First Question

A bear walks south for one kilometer, then it walks west for one kilometer, then it walks north for one kilometer and ends up at the same point from which it started. What color was the bear?

Last edited: Jan 10, 2007
2. Jan 10, 2007

### dontdisturbmycircles

He must have been standing at the north pole in order to arrive at the same point. Thus he was white because he was a polar bear? lol.

3. Jan 10, 2007

### Hootenanny

Staff Emeritus

4. Jan 10, 2007

### neutrino

>>White - It's a polar bear, and it probably started walking from the north pole. <<

I don't have any interesting brain teasers right now . Can I let someone else post a question? (in the case that I've posted the correct answer before anyone else does)

(Just can't resist answering questions, you know )

5. Jan 10, 2007

### neutrino

Great! I have the right answer and I don't have to post a questions!

Edit: Why can't it be a brown bear, or black bear that was transferred to the Arctic for some experiment?

6. Jan 10, 2007

### dontdisturbmycircles

I am going to need to be solving this as you are... I was caught unprepared lol, but I found one that looks sorta interesting, so here goes.

In the city of Funkytown, the following facts are true:

No two inhabitants have exactly the same number of hairs.
No inhabitant has exactly 483,207 hairs.
There are more inhabitants than there are hairs on the head of any one inhabitant.
What is the largest possible number of inhabitants of Funkytown?

7. Jan 10, 2007

### dontdisturbmycircles

I think this riddle is a dud, I don't see a limit? lol am I just tired?

8. Jan 10, 2007

### Hootenanny

Staff Emeritus
I think I have it. The riddle states that there is no one with 483,207 hairs, therefore we can say that there may be 483,207 inhabitants with between [0, 483 206] hairs on their head. However, if there were more than 483,207 inhabitants this would violate the third condition. Therefore, the maximum number of inhabitants is 483,207.

What say you?

9. Jan 10, 2007

### dontdisturbmycircles

I see the answer as being 0. In the minimum case there is 1 man with 1 hair, that causes there to also be another man with more than one hair, which causes there to be another man with more than 2 hairs, add infinitum. So 0 is the only plausible answer.

10. Jan 10, 2007

### neutrino

That was nice.

edit: How about this case, one man with one hair, and another, who is bald. Conditions satisfied, no?

edit2: Is it specified that there are no bald inhabitants?

Last edited: Jan 10, 2007
11. Jan 10, 2007

### dontdisturbmycircles

edit:double post

12. Jan 10, 2007

### dontdisturbmycircles

Makes sense to me, your turn. Thank god, I can go to sleep now. Good night! :-)

I didn't even think of including a bald guy. lol

If every man had at least 1 hair, then 0 would be right. :P

Last edited: Jan 10, 2007
13. Jan 10, 2007

### Hootenanny

Staff Emeritus

Anyway the next teaser;

Find the remainder if we divide ${\color{blue}1!+2!+3!+\ldots +100!}$ by 7

Last edited: Jan 10, 2007
14. Jan 10, 2007

### neutrino

Thankfully, there is a weekly that we subscribe to which has this little teaser in every issue. Most of them are simple enough.

Fill in the blank so that line 4 is consistent with the first three.

Triangle, Pentagon, Square

Square, Hexagon, Hexagon, Square

Pentagon, Hexagon, Hexagon, Hexagon, Square, Triangle

Hexagon, Octagon, Octagon, Octagon, Octagon, __________

15. Jan 10, 2007

### Hootenanny

Staff Emeritus
Except we are to find the maximum number of inhabitants.

16. Jan 10, 2007

### neutrino

Oops! Didn't notice Hoot's post. I though 'circles was referring to me.

Anyway, I'm not planning to delete the stuff I typed. :tongue2: You can solve this, too, "outside" the game.

17. Jan 10, 2007

### davee123

Since all the terms from 7! to 100! are evenly dividisble by 7, we only need to find the remainder of (1!+2!+3!+4!+5!+6!)/7, which is 5 :)

DaveE

18. Jan 10, 2007

### dontdisturbmycircles

edit:woops I did this wrong, lol. I really need to go to bed. goodnight

Last edited: Jan 10, 2007
19. Jan 10, 2007

### Hootenanny

Staff Emeritus