Brainteaser (this may be old, but it's new to me)

That is not correct. Once a choice is eliminated the probabilities change.

 

This puzzle has always confused me, which is why I gave a joke answer to begin with.

The key to knowing is the host. Does the host have a choice in which curtain to open? The host always knows which curtain does not have a prize behind it.

If you choose the correct door, the host will then have two choices of which curtain to show you that there is no prize behind.

If you choose the wrong door, the host will only have one choice - the other incorrect door... curtain... whatever.

That's why I gave my answer - try to get a read on the host. Most gameshow hosts out there want you to win the prize. If he seems conflicted at all in which door he should reveal before the your final decision, then you know you have chosen the correct one and should NOT switch.

However, I tend to side with jkj (sorry Frozo) in that if you have no other information, you switch curtains/doors, as the probability with that being the correct door is now 2/3 and not 1/3.

I know it sounds crazy, but aren't most of the puzzles posted here crazy?

 

Yes, the probabilities change to 1/3 and 2/3 not to 1/2 and 1/2.

If I choose curtain A, the host is ALWAYS going to open B or C. There is always at least one empty one remaining. Since I don't know if I made the right choice, I don't know if the host's choice is random or forced. In either case it says nothing about curtain A.

Since no new information can be obtained about A the probability remains the same for A. The only new information is about B and C.

Or enumerating the possibilities. Let's say the prize is in C. Let's say 1 is my choice (before a possible switch) and 2 is the host's choice.

ABC Prob my pick Prob of host's pick Total probability
---- ------------ ----------------- ---------------
12x 1/3 1/1 (only one choice) 1/3
1x2 1/3 0/1 (not allowed) 0/3
x12 1/3 0/1 (not allowed) 0/3
21x 1/3 1/1 (only one choice) 1/3
2x1 1/3 1/2 (two possibilities) 1/6
x21 1/3 1/2 (two possibilities) 1/6

In the first and second case you should switch. There is a 2/3 chance (1/3 + 1/3) of encountering one of these two.

In the last two cases you should keep your pick. There is a 1/3 chance (1/6 + 1/6) of encountering one of these two.

 

EDIT: I hated the way I worded that question, so I'm gonna just start from scratch...

Texas is getting killed against OU. The Sooners are up 14 and it's the fourth quarter. However, sheer dumb luck (VY, anyone?) caused them to actually score a touchdown!

Now, it's decision time for Mack Brown - does he go for one point, which is a gimmie, or does he go for two?

Mack Brown decides that he will go for one here just to get the point, but vows that the next time they score, they'll go for two to beat the Sooners outright.

Do you agree with Mack Daddy's decision?

 

Assuming OU isn't going to score again complicating things, he should try for 2 points the first time. If he misses it, he can try for 2 again to tie the game.

If he kicks the extra point first, and misses the 2 point conversion later, he can't go back and change the original extra point into a 2 point conversion.


Is that better, Badger?

 

Argh... now everyone can see my original

Oh well, In any event, next!

Some evil culprit ate T. Boone Pickens' T-Bone steak. Bone Picker has lined up the three suspects - AD Mike Holder, Man, 41 Mike Gundy, and basketballer Travesty Ford for questioning:

Mike Holder: I ate it, and I LOVED it!
Mike Gundy: I saw Holder eat it.
Travesty Ford: Gundy and I didn't eat it!

T. Booner might not have seen the oil price dropage coming, but he can see that one of his three stooges is lying. Which one is it, and why?

 

See, these kick my butt. If there's only one liar, based on Holder alone, we invalidate the whole thing by assigning True/False variables to each stooge. Example being...

If Holder = True then Gundy = True, Ford = True.

Invalidating the statement. However...

If Holder = False then Gundy = False and Ford = False based on Holder = False because either Gundy or Ford ate the steak.

Maybe I'm just not seeing it right. But with the stipulation that there's only ONE liar, establishing that there must be TWO truths, I can't see how the scenario works.

 

Since you so wonderfully revived this thread, I'll give you a hint - t-bone steaks are too large for just one to eat

 

If THAT'S the case then, Ford is the liar. Ford and Holder ate the steak. Multiple steak eaters never entered my mind.

Holder = True
Gundy = True

Leaving by deduction plus the new information, Ford = False because we need one liar, but multiple steak eaters.

 

Well, let's try your hand at a number puzzle, shall we?

In an effort to appear like a legit academic institution to the NCAA allegations committee, UConn stole Oklahoma's "magic square." Unfortunately, in the process of stealing said 3 by 3 square, most of the numbers fell out!

2 [] []
[] [] []
[] 1 []

The square is useless unless the numbers are all in place, when the numbers added together horizontally, vertically or diagonally will all equal the same digit.

Place 3,4,5,6,7,8,9 so that OU's square is magical once again! UConn will surely be doomed to years of probation without it!

 

Good, but I liked the answer the guy in the movie "21" gave a little better.

 

2 9 4
7 5 3
6 1 8

err don't we want Uconn to go on probation?