Author Topic: Pizza brainteaser - here is another (Read 2553 times)

scott123 · « **Reply #20 on:** August 22, 2012, 06:29:49 PM »

This is pretty well known probability exercise. You always should choose the box you didn't pick, as your odds improve. I think this was on mythbusters.

TXCraig1 · « **Reply #21 on:** August 22, 2012, 06:31:01 PM »

If you are correct, what is the pobability of success and why?

pizzaneer · « **Reply #22 on:** August 22, 2012, 06:38:54 PM »

While you silly humans were messing about with psychology kung-fu, Hulk smashed the vending machine and ate the pizza. He said it was ok, but not as good as Craig's.

I recall a test close to this given to lab rats in a Stanford experiment. The rats that chose a different box, no matter what box they started with had a better success rate. No one could explain it, and it's always puzzled me, since it should be a straight-up flip of the coin. 50% will get the pizza, 50% won't, but oddly, taking a further action seemed to turn the odds in favor of the risk-takers. Final tally was about 53% to 47%, I think. Marginal but significant.

TXCraig1 · « **Reply #23 on:** August 22, 2012, 06:40:45 PM »

There is a definite, logical answer.

TXCraig1 · « **Reply #24 on:** August 22, 2012, 06:42:25 PM »

Bill solved the first one in about 30 seconds. Where is he now???

bfguilford · « **Reply #25 on:** August 22, 2012, 06:45:19 PM »

Quote from: TXCraig1 on August 22, 2012, 06:42:25 PM

Bill solved the first one in about 30 seconds. Where is he now???

He's enjoying the 8 slices from the last pie. Either that, or his hand got stuck in one of the boxes.

scott123 · « **Reply #26 on:** August 22, 2012, 06:45:42 PM »

Here you go, Brian, I'll give you a hint. It should be REALLY easy after this

Pete-zza · « **Reply #27 on:** August 22, 2012, 06:57:03 PM »

Craig,

I did not look at the math that scott123 posted. If there are three boxes and only one of them has a pizza in it, whether you know that or not, then the odds are one in three. If you can only make one pick, and you know that only one of the two remaining boxes contains the pizza because the manager told you that, that doesn't tell you which of the remaining two boxes to pick. So, with only one pick, the odds remain the same, one in three.

Peter

Jet_deck · « **Reply #28 on:** August 22, 2012, 07:01:06 PM »

But if the manager tells you that one of boxes is not the one the it becomes one of two possibilities, no?

cornicione54 · « **Reply #29 on:** August 22, 2012, 07:17:58 PM »

The pizza has not moved. Since the probability for choosing one box out of three is 1/3, switching leaves you with the remaining odds 2/3 - or at least that's a (my) simplistic way of looking at it.
You double your odds by switching.

SquirrelFlight · « **Reply #30 on:** August 22, 2012, 07:26:59 PM »

This is one of the "classic" exercises in probablilty theory. I'll have to go lookup the details, but if I remember it correctly, it isn't 50/50: you have a higher probability of getting the pizza if you change your choice compared to keeping your original choice. If you only get to open one box, you won't be able to determine 100% where the pizza is.

pizzaneer · « **Reply #31 on:** August 22, 2012, 07:39:58 PM »

Quote from: cornicione54 on August 22, 2012, 07:17:58 PM

The pizza has not moved. Since the probability for choosing one box out of three is 1/3, switching leaves you with the remaining odds 2/3 - or at least that's a (my) simplistic way of looking at it.
You double your odds by switching.

This is correct. Viewed as an overall sum, by switching your final choice, you will double your chance of winning to 2/3.

I still maintain that if viewed as a discrete probability node, the chance is 50/50. But then, it's probably a good thing I don't go to Vegas.

Good one, Craig!

scott123 · « **Reply #32 on:** August 22, 2012, 08:06:09 PM »

See, I knew once I gave you the formula, you could solve it. You're welcome

pizzaneer · « **Reply #33 on:** August 22, 2012, 08:13:59 PM »

Quote from: scott123 on August 22, 2012, 08:06:09 PM

See, I knew once I gave you the formula, you could solve it. You're welcome

Yeah buddy. I can't take credit for it though. The name of the .jpg was a giveaway.

Jet_deck · « **Reply #34 on:** August 22, 2012, 08:19:44 PM »

Oh, so by eliminating one of the possible boxes and it not being the one you have in hand, it matters?

Jet_deck · « **Reply #35 on:** August 22, 2012, 08:22:13 PM »

Quote from: cornicione54 on August 22, 2012, 07:17:58 PM

The pizza has not moved. Since the probability for choosing one box out of three is 1/3, switching leaves you with the remaining odds 2/3 - or at least that's a (my) simplistic way of looking at it.
You double your odds by switching.

If he is telling the truth, the one box should not be a choice, so one of two?

What if he said the one in hand is empty, you still have 2 to choose from.

Jet_deck · « **Reply #36 on:** August 22, 2012, 08:25:08 PM »

Quote from: TXCraig1 on August 22, 2012, 06:40:45 PM

There is a definite, logical answer.

Yeah, just like the Hampton being at walking distance from the summit. The Calabrian chili oil must be eating at your brain.

cornicione54 · « **Reply #37 on:** August 22, 2012, 08:28:53 PM »

OK here's one:

1. There are 5 houses (along the street) in 5 different colours: beige, brown, grey, orange, purple.
2. On this street live 5 pizza makers: Bill, Chau, Craig, Norma and Peter
3. These 5 pizza makers each drink a certain beverage: Beer, Chateau Mouton, Limoncello, Tea and Water.
4. They each have a specific oven: Electric Oven, Gas Oven, Pizza Grill Insert, LBE and a WFO
5. They each make a specific type of pizza: NY Style, Cracker Style, Sicilian Style, New Haven and Vera Pizza Napoletana

None of the pizza makers have the same oven, make the same style of pizza or drink the same beverage.

Hints:
1. Craig lives in an orange house.
2. Peter makes Sicilian Style
3. Bill drinks tea.
4. The brown house is on the left of the beige house (next to it).
5. The brown house owner drinks Chateau Mouton.
6. The person with a pizza grill insert makes cracker style pizza.
7. The owner of the grey house has a gas oven
8. The person living in the house right in the center drinks limoncello.
9. Norma lives in the first house.
10. The person with a WFO lives next to the one who makes NY style pizza..
11. The person who makes New Haven pizza lives next to the person with a gas oven.
12. The owner of the electric oven drinks beer.
13. Chau has a LBE
14. Norma lives next to the purple house.
15. The person with a WFO has a neighbour who drinks water.

Who makes authentic neapolitan pizza?

scott123 · « **Reply #38 on:** August 22, 2012, 08:32:28 PM »

Bill, Chau, Craig, Norma and Peter, I can't expressed how disappointed I am that one of you wasted the money on a Pizza Grill Insert

Bill/SFNM · « **Reply #39 on:** August 22, 2012, 08:43:35 PM »

Is this a trick question or am I gonna have to take out a pencil? I don't think I own a pencil anymore. Maybe it's in the drawer with the slide rule.