Brain Teasers Q&A Game

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Main Question or Discussion Point

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?

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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.

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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.

>>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 )

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?

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?

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

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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?

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.

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.
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?

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edit:double post

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

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

Anyway the next teaser;

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

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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, __________

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edit: How about this case, one man with one hair, and another, who is bald. Conditions satisfied, no?
Except we are to find the maximum number of inhabitants.

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.

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

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

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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
I am just now learning about factorial stuff, but I think I can answer this. Noting that all numbers above 7! are divisible by 7, we have 1! 2!... 6! to deal with

$$\frac{1!+2!+3!...6!}{7}=124.7$$

edit:woops derr I did this wrong, I was supposed to take the remainder of each term. lol. I really need to go to bed. goodnight

Alright... What letter comes next?

o, e, o, e, r, e, x, ?

DaveE

Alright... What letter comes next?

o, e, o, e, r, e, x, ?

DaveE
Well, the last six letters are the last letters of numbers in a row eg. x is the last letter of six, e is the last letter of five, r is the last letter of four and e is the last letter of three, o is the last letter of two, e is the last letter of e. However, I'm not sure what the first o stands for.

If I continue this series, then I would get an n since that is the last letter in the number seven?

Edit: o is the last letter in zero

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Well, the last six letters are the last letters of numbers in a row eg. x is the last letter of six, e is the last letter of five, r is the last letter of four and e is the last letter of three, o is the last letter of two, e is the last letter of e. However, I'm not sure what the first o stands for.

If I continue this series, then I would get an n since that is the last letter in the number seven?

Edit: o is the last letter in zero
Exactly! I hoped the "zero" might throw people off. I was actually tempted to start the sequence at "negative three", yielding:

e, o, e, o, e, o, e, r, e, x

But I figured that might be a bit too confusing and arbitrary.

DaveE

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, __________
This one was a pain in the a-- :-). When I first saw it I thought that it would have to do with Pascal's triangle, but within 30 seconds it became apparent that it didn't. Eventually I noticed the first shape always has one more side than in the sentence before it. So perhaps it is just a number used to make a list. Then I noticed that 3 was dividible by 9, and then it was easy to tie it all together.

Square.

3^2 [5+4]

4^2 [6+6+4]

5^2 [6+6+6+4+3]

6^2 [8+8+8+8+4]

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I have a feeling that Moridin won't be back.

Square.

3^2 [5+4]

4^2 [6+6+4]

5^2 [6+6+6+4+3]

6^2 [8+8+8+8+4]