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PUZZLES and PUZZLES GALORE!

Dang it Chad!!!! Every time I go to post, you've already done it.....
 
*********COPY EVERYTHING BETWEEN THIS AND THE BOTTOM LINE**********

SIX THE HARD WAY

(0!+ 0!+ 0!)! = 6

(1+ 1+ 1)! = 6

2 + 2 + 2 = 6

3 x 3 - 3 = 6

√4 + √4+ √4 = 6

5 / 5 + 5 = 6

6 + 6 - 6 = 6

7 - 7 / 7 = 6

8 - √(√(8 + 8)) = 6

√9 X √9 - √9 = 6

*******************
 
DING DING DING! WE HAVE A WINNAH!

Awesome job, guys!

If you have a puzzle to share, KJ, the floor is yours.

I edited the title so we won't have to limit this to just number puzzles, any brainteaser will do.
 
Thanks, Chad! I needed the factorial hint when I first learned it, but then again my last math class was in 1993, lol!

My last math class was in 2010. Although my wife is currently in school for her master's degree for education with an emphasis on math
 
OK, Here's a good one that took me a while to figure out. Again, no cheating, and if you've heard the puzzle before, please allow others to solve it.

There is a prison that houses 11 prisoners. The warden has agreed to release all the prisoners if they can solve his puzzle. If they are incorrect, they will be executed.

The prisoners are all kept solitarily, and cannot see or hear any of the other prisoners at any time. There is a room, that has two switches. A and B. Each switch has 2 positions, Up or Down. The switches are not connected to anything. The prisoners will be selected randomly at random intervals and taken into the room. (They could be selected several times in a row, and could be days or years inbetween selections). Once in the room they must flip one, and only one, of the switches. Either one they choose. The initial position of the switches is random and unknown.

The object it to identify when ALL 11 of the prisoners have been to the room, at least once. Any prisoner may answer when they feel confident, but if they are wrong..... execution! They will have 10 minutes to strategize, before it begins. After that, they will be completely cut off from each other again. How will they survive this challenge and be released?
 
I just stop in here and it's smells like chalk dust! Stand back boys, they're doin' math!
 
OK, Here's a good one that took me a while to figure out. Again, no cheating, and if you've heard the puzzle before, please allow others to solve it.

There is a prison that houses 11 prisoners. The warden has agreed to release all the prisoners if they can solve his puzzle. If they are incorrect, they will be executed.

The prisoners are all kept solitarily, and cannot see or hear any of the other prisoners at any time. There is a room, that has two switches. A and B. Each switch has 2 positions, Up or Down. The switches are not connected to anything. The prisoners will be selected randomly at random intervals and taken into the room. (They could be selected several times in a row, and could be days or years inbetween selections). Once in the room they must flip one, and only one, of the switches. Either one they choose. The initial position of the switches is random and unknown.

The object it to identify when ALL 11 of the prisoners have been to the room, at least once. Any prisoner may answer when they feel confident, but if they are wrong..... execution! They will have 10 minutes to strategize, before it begins. After that, they will be completely cut off from each other again. How will they survive this challenge and be released?

OOOOH, this is a good one. I have heard it before, so I will let the rest of the fellas take a crack
 
These are my kinda problems. Where it hurts your brain figuring it out. I know I hear it some time ago, but my brain doesn't remember things.
 
I just stop in here and it's smells like chalk dust! Stand back boys, they're doin' math!
I'm with you Dave, I liked math until I graduated in 82 and haven't really used it since inthe realm they're using it. Y'all to smart for me. I need dummer friends. I've heard this one before too and forgot the answer.......back to work for me
 
I'm with you Dave, I liked math until I graduated in 82 and haven't really used it since inthe realm they're using it. Y'all to smart for me. I need dummer friends. I've heard this one before too and forgot the answer.......back to work for me

Work?!

Whats more important, work or helping save the lives of 11 people? Seriously Dave! ?
 
I feel like I'm missing something. Well, obviously if I haven't figured it out.

Lemmie get this straight. So in theory, once everyone has been in the room at least once, the next person going in should be able to determine they have because of the position of the switches. But the position is random on each person entering, which means the position of the switches shouldn't imply anything. So it's not really about the switches.
 
Oh wait, the INITIAL position is random, not before each person...
 
Right now any potential system I can think of breaks down when prisoners can be randomly selected to go again before they have all be through once.
 
Lemmie get this straight. So in theory, once everyone has been in the room at least once, the next person going in should be able to determine they have because of the position of the switches. But the position is random on each person entering, which means the position of the switches shouldn't imply anything. So it's not really about the switches.
It's all about the switches!

Oh wait, the INITIAL position is random, not before each person...

Right, so initially they could both be up, both down, or 1 up and 1 down. But the prisoner are the ONLY ones who will be flipping switches. The guards/warden will not interfere after it has started.
 
This is one of those puzzles that, once you know the answer and think about it for a minute, you feel like it makes perfect sense, but until you get there you just wrack your brain trying to make heads or tails of it. The fact that the prisoners get to come up with a strategy among themselves is critical.
 
And just a pro tip, puzzles like these are great to use in bar situations, because people will often get so flummoxed that they will gladly buy you a drink for you to give them the answer!
 
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