Tough "logic" problem -- can you get it?

[Dan Druff]

I saw it posted on Facebook, and I worked it out without looking up the answer.

It's very interesting.

Don't cheat.

[Benford]

I saw it posted on Facebook, and I worked it out without looking up the answer.

It's very interesting.

Don't cheat.

Solved it in less than 5 minutes. It's a great problem. The guy who wrote the problem should be a pro poker player!

[SrslySirius]

 

The only way Bernard could know for sure is if it fell on the 18th or 19th, since those days only show up once. For Albert to be certain that Bernard couldn't have received one of those dates, he must have ruled out May and June.

So Bernard knows that Albert must have been told July or August. If Bernard was told 14th, this isn't helpful. If he was told 15th, 16th or 17th, he should now know the exact date.

So with Bernard having the correct answer, Albert knows it must be the 15th 16th or 17th. These fall on different months, so he simply chooses the one corresponding to whichever month he was told.

EDIT: nvm, August comes up twice. If Albert was was told August, he still won't be sure. He must have been told July, and confirmed that her birthday is July 16th.

[Benford]

Answer...

Congrats, you solved it! But...maybe a spoiler tag for future visitors who want to work it out?

[SrslySirius]

This reminds me of one of my favorite logic puzzles.

A teacher decides to test his three top pupils to see which is the brightest. He tells them "I will paint a dot on each of your foreheads. It will be either green or red. If you see a red dot, you must raise your hand. The first person to determine the color of their own dot wins."

The teacher puts a red dot on all three of them. All students raise their hands and begin thinking. After about three seconds, one student proclaims "I have a red dot on my forehead."

How does he know?

[4Dragons]

This reminds me of one of my favorite logic puzzles.

A teacher decides to test his three top pupils to see which is the brightest. He tells them "I will paint a dot on each of your foreheads. It will be either green or red. If you see a red dot, you must raise your hand. The first person to determine the color of their own dot wins."

The teacher puts a red dot on all three of them. All students raise their hands and begin thinking. After about three seconds, one student proclaims "I have a red dot on my forehead."

How does he know?

The answer had better not be 'they all live in India'

[Zap_the_Fractions_Giraffe]

lol didn't try

[Dan Druff]

This reminds me of one of my favorite logic puzzles.

A teacher decides to test his three top pupils to see which is the brightest. He tells them "I will paint a dot on each of your foreheads. It will be either green or red. If you see a red dot, you must raise your hand. The first person to determine the color of their own dot wins."

The teacher puts a red dot on all three of them. All students raise their hands and begin thinking. After about three seconds, one student proclaims "I have a red dot on my forehead."

How does he know?

I don't like this one because it's a trick question.

I gave up on it and finally looked up the answer:

 

The answer involves the guy who spoke up knowing that his had to be red, because nobody else had spoken up yet.

If his was blue, then the other two smart students would have immediately figured out their own color by process of elimination. Since both other students sat there for 3 seconds not answering, he knew they couldn't get it quickly and obviously by looking at his, so his had to be red (requiring a lot more thought).

The reason I don't like this is because it assumes that both other students would have figured out the "obvious" answer within 3 seconds, which isn't necessarily true. I think more emphasis has to be put on the amount of time passing -- like perhaps 60 seconds or more.

[SrslySirius]

I don't like this one because it's a trick question.

I gave up on it and finally looked up the answer:

 

The answer involves the guy who spoke up knowing that his had to be red, because nobody else had spoken up yet.

If his was blue, then the other two smart students would have immediately figured out their own color by process of elimination. Since both other students sat there for 3 seconds not answering, he knew they couldn't get it quickly and obviously by looking at his, so his had to be red (requiring a lot more thought).

The reason I don't like this is because it assumes that both other students would have figured out the "obvious" answer within 3 seconds, which isn't necessarily true. I think more emphasis has to be put on the amount of time passing -- like perhaps 60 seconds or more.

I disagree.

 

Mentioning that the students are smart helps, but it's not really required. If the other two students are even of average intelligence, and your dot is blue, they should be shouting an answer immediately.

Imagine seeing one blue dot and one red. The guy with the red dot has his hand raised. Why is his hand raised? Where could he be seeing a red dot? He can't see his own forehead. You would know immediately that you're wearing a red dot. It would be completely obvious. Three seconds is more than enough time to realize this. 10 seconds would be generous. 60 certainly is not necessary.

Maybe 3 seconds is too fast for the genius kid to figure it all out. Next time I tell this riddle, I'll go with 10.

[superallah]

I don't like this one because it's a trick question.

I gave up on it and finally looked up the answer:

 

The answer involves the guy who spoke up knowing that his had to be red, because nobody else had spoken up yet.

If his was blue, then the other two smart students would have immediately figured out their own color by process of elimination. Since both other students sat there for 3 seconds not answering, he knew they couldn't get it quickly and obviously by looking at his, so his had to be red (requiring a lot more thought).

The reason I don't like this is because it assumes that both other students would have figured out the "obvious" answer within 3 seconds, which isn't necessarily true. I think more emphasis has to be put on the amount of time passing -- like perhaps 60 seconds or more.

I disagree.

 

Mentioning that the students are smart helps, but it's not really required. If the other two students are even of average intelligence, and your dot is blue, they should be shouting an answer immediately.

Imagine seeing one blue dot and one red. The guy with the red dot has his hand raised. Why is his hand raised? Where could he be seeing a red dot? He can't see his own forehead. You would know immediately that you're wearing a red dot. It would be completely obvious. Three seconds is more than enough time to realize this. 10 seconds would be generous. 60 certainly is not necessary.

Maybe 3 seconds is too fast for the genius kid to figure it all out. Next time I tell this riddle, I'll go with 10.

i agree.

 

[Pooh]

I disagree.

 

Mentioning that the students are smart helps, but it's not really required. If the other two students are even of average intelligence, and your dot is blue, they should be shouting an answer immediately.

Imagine seeing one blue dot and one red. The guy with the red dot has his hand raised. Why is his hand raised? Where could he be seeing a red dot? He can't see his own forehead. You would know immediately that you're wearing a red dot. It would be completely obvious. Three seconds is more than enough time to realize this. 10 seconds would be generous. 60 certainly is not necessary.

Maybe 3 seconds is too fast for the genius kid to figure it all out. Next time I tell this riddle, I'll go with 10.

i agree.

 

Is that marty?

[Benford]

The world-famous "Monty Hall Problem" deserves a mention here. Without cheating, is it advantageous to switch your chosen door (explained below)? Why or why not?

From Priceonomics website:

Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

“Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”

Statistically, which choice gets you the car: keeping your original door, or switching?


Marilyn vos Savant (billed as the world's smartest woman with an IQ of almost 200) answered the problem correctly in an issue of Parade magazine. Thousands of people responded by mistakenly telling her she was wrong, including a sizeable contingent of Ph.D.'s in mathematics.

[SrslySirius]

Every time I see the Monty Hall problem brought up, there's always someone refusing to accept the answer. If that's you, Numberphile has a decent video breaking it down.

 

If you still don't believe it, PM me and let's play for real money. =D

[smithbk]

I don't like this one because it's a trick question.

I gave up on it and finally looked up the answer:

 

The answer involves the guy who spoke up knowing that his had to be red, because nobody else had spoken up yet.

If his was blue, then the other two smart students would have immediately figured out their own color by process of elimination. Since both other students sat there for 3 seconds not answering, he knew they couldn't get it quickly and obviously by looking at his, so his had to be red (requiring a lot more thought).

The reason I don't like this is because it assumes that both other students would have figured out the "obvious" answer within 3 seconds, which isn't necessarily true. I think more emphasis has to be put on the amount of time passing -- like perhaps 60 seconds or more.

I disagree.

 

Mentioning that the students are smart helps, but it's not really required. If the other two students are even of average intelligence, and your dot is blue, they should be shouting an answer immediately.

Imagine seeing one blue dot and one red. The guy with the red dot has his hand raised. Why is his hand raised? Where could he be seeing a red dot? He can't see his own forehead. You would know immediately that you're wearing a red dot. It would be completely obvious. Three seconds is more than enough time to realize this. 10 seconds would be generous. 60 certainly is not necessary.

Maybe 3 seconds is too fast for the genius kid to figure it all out. Next time I tell this riddle, I'll go with 10.

The only part I don't understand is how the dot turns from green in the question to blue in the answer.

As is the case in many questions of logic, pretend one member had the opposite of the original statement and work out what happens.

 

In this case, pretend you are in the middle with a green dot. If the other two see their respective red dots, sure they raise their hands. If you have a green dot, they should be able to work out quickly that they each have a red dot because the OTHER other one raised a hand... but they don't.

[Brittney Griner's Clit]

Easiest way for me to understand the Monty hall which I read over 4 times and didn't get...

Let's say he asks you to pick one door... then without opening any of the other two doors he asks you if you want to keep your door or switch to the other two.

[herbertstemple]

Every time I see the Monty Hall problem brought up, there's always someone refusing to accept the answer. If that's you, Numberphile has a decent video breaking it down.

 

If you still don't believe it, PM me and let's play for real money. =D

Watched the video.

The math makes sense.

Have you ever done this to see if it really works SS? 1/2 to 2/3 is such a difference that it shouldn't too long to prove. A few hundred sessions should be enough.

Still skeptical about this.

Still don't get how you figured the original problem.

[SrslySirius]

Watched the video.

The math makes sense.

Have you ever done this to see if it really works SS? 1/2 to 2/3 is such a difference that it shouldn't too long to prove. A few hundred sessions should be enough.

Still skeptical about this.

Still don't get how you figured the original problem.

I haven't myself, but monte carlo simulations have been done. They turn out as you would expect.

Every step of the problem Druff posted can be worked out by asking "how does he know what he says he knows?"

[SrslySirius]

Actually, we can just do it right now. I'll go to random.org and tell it to pick a random integer 1-3 a hundred times. This will represent which door contains the prize.

For this simulation, we're starting with door #1 every time. So if you're a stayer, every 1 in the list is a winner. If you're a switcher, every 2 and 3 is a win. Like BGC said, switching means I'm essentially picking both doors. One of them will be revealed to be a goat, so my only choice is to pick what's left.

 

Random Integer Generator

Here are your random numbers:

1 1 1 3 3
1 2 2 1 1
3 1 3 1 3
2 1 2 2 2
3 3 1 1 2
2 2 3 2 2
1 1 2 3 2
2 1 1 2 3
3 3 2 1 1
3 1 2 3 1
3 2 2 1 1
1 1 1 2 2
1 3 3 3 3
1 3 2 1 3
2 1 1 2 2
1 2 3 1 1
2 2 2 3 3
1 3 1 1 2
2 3 1 1 1
2 2 3 3 1
Timestamp: 2015-04-15 18:58:31 UTC

In this simulation, switchers win 61-39. Kind of a bad run actually.

[Benford]

Easiest way for me to understand the Monty hall which I read over 4 times and didn't get...

Let's say he asks you to pick one door... then without opening any of the other two doors he asks you if you want to keep your door or switch to the other two.

If Monty does not open any of the other two doors, there would be no advantage to switching doors over sitting tight. Your odds of winning the car are the same either way.

It's only when Monty actually opens one door showing a goat after you chose your own door (revealing new information.....like another card being shown in a poker game) does it become an advantage to switch doors for the car.

[SrslySirius]

If Monty does not open any of the other two doors, there would be no advantage to switching doors over sitting tight. Your odds of winning the car are the same either way.

It's only when Monty actually opens one door showing a goat after you chose your own door (revealing new information.....like another card being shown in a poker game) does it become an advantage to switch doors for the car.

It's the same thing mathematically, a 2/3 chance. In the 100 door example, this is like Monty saying "Okay, you've got door #1. You can stick with that, or you can just take whatever is behind doors 2 through 100." Either is a 99% chance of getting the car.