Logic Problem Problem

[Tom Sawyer]

Many of you may be aware of the logic problem that's going around the internet about that bitch Cheryl who pissed off all her friends so they decided not to come to her birthday party.

http://gawker.com/can-you-solve-the-math-problem-that-has-torn-singapore-1697828833/+charliejane

One thing I can't wrap my head around in all the explanations is the rationale used to eliminate the entire months of May and June. Can someone provide an explanation for that - perhaps using puppets? I've read three or four and it still seems like an unwarranted leap of logic to me.

 

[beero1000]

Albert knows only the month of Cheryl's birthday and Bernard knows only the date of Cheryl's birthday. Importantly, both know that each knows their respective parts.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know too.
Translation: The month of Cheryl's birthday is represented multiple times in the list, so since I only know the month, I can't figure out the exact date. On the other hand, the dates for the month I know are each represented multiple times in the list, so Bernard can't figure out the exact birthday either.

Conclusion: May cannot be the month of the birthday, because 19 only appears on the list for May 19th. If the month was May, Albert would not be able to definitively say that he knows that Bernard does not know the exact birthday because the birthday might be May 19th. If the birthday was May 19th, then Bernard would immediately know the exact birthday because Cheryl told him her birthday is on a 19th, and May 19th is the only 19th on the list. Similarly, the month cannot be June because Bernard would immediately know that the 18th Cheryl meant was June 18th.

 

[Tom Sawyer]

OK, it was the definitiveness of Albert's statement that I was missing. Thanks, dude!

 

[Juma]

A knows that B doesnt know. How? Because A know that for the month he was told there is no unique dates. Thus the month cannot be may or june since both have unique dates (19 for may and 18 for june)

Oh. Late to the party...

 

[bilby]

Who cares when she was born? I want to know what colour her fucking dress is.

 

[fromderinside]

Who cares when she was born? I want to know what colour her fucking dress is.

It was gold not blue and black.

 

[beero1000]

In the same spirit, Tanya Khovanova posted the following puzzle on her math blog.

I thought of a positive integer that is below 100 and is divisible by 7. In addition to the public knowledge above, I privately tell the units digit of my number to Alice and the tens digit to Bob. Alice and Bob are very logical people, but their conversation might seem strange:

Alice: You do not know Tanya’s number.
Bob: I know Tanya’s number.


What is my number?

 

[bilby]

In the same spirit, Tanya Khovanova posted the following puzzle on her math blog.

I thought of a positive integer that is below 100 and is divisible by 7. In addition to the public knowledge above, I privately tell the units digit of my number to Alice and the tens digit to Bob. Alice and Bob are very logical people, but their conversation might seem strange:

Alice: You do not know Tanya’s number.
Bob: I know Tanya’s number.


What is my number?

I worked out Tanya's number; but she is not answering

I think the area code is missing.

Show

Her number is 70

 

[Kharakov]

In the same spirit, Tanya Khovanova posted the following puzzle on her math blog.

Show

Her number is 70

Show

The tens digit of 7 is 0, so how did they know who had the 10s or the 1s?
All the digits, except for 2, appear in both columns.
There is no way the person getting the units column could know that they have the units column.
The person getting the tens column could know they received the 10s column if they received a 2.

 

[bilby]

Show

Her number is 70

Show

The tens digit of 7 is 0, so how did they know who had the 10s or the 1s?
All the digits, except for 2, appear in both columns.
There is no way the person getting the units column could know that they have the units column.
The person getting the tens column could know they received the 10s column if they received a 2.

Show

The way I read the problem, Alice knows she is getting the units, and that Bob gets the tens.

Alice then says that Bob doesn't know - so Bob knows that the answer is a number for which there are two possible answers with the same tens digit. 21 and 28; 42 and 49; 70 and 77 or 91 and 98. But Bob then knows the answer - and the only way this is possible is if his tens digit is a seven. Because if the answer was 77, Alice could not have been certain he didn't know the answer - she would know it was 07 or 77, and if it was 07, he would know it.

If the unit is 0, then Bob must have a 7 for the tens. With just a 7, Bob knows of two possible answers, but knowing that Alice does not have a seven, he can eliminate 77 and is left with the answer - 70

 

[Kharakov]

Show

I skipped 42 in my analysis of the integer sequence, which is the answer to life, the universe, and everything, so is technically correct.

Still not sure they are supposed to know whether they are getting the tens or units. I suppose if there is no logical way for them to know without being told which has which, then Bob couldn't have known the answer.

 

[beero1000]

Is it time to fire up the math quiz thread again?

 

[Kharakov]

Probably. I've had tori on my mind. I was messing with a torus based Mandelbulb formula (instead of sphere (degenerate torus) based formula).

 

[fromderinside]

You're so smart. Swoon./need examples.

 

[braces_for_impact]

The real question is this: How many friends does Cheryl currently have? The answer is FUCKING ZERO.

 

[Kharakov]

need examples.

It was basically crap, some semi interesting stuff occurred, but no breakthrough. Pretty sure someone probably tried it out in the past anyway. One last idea is to try altering the 3d burning ship formula, see if more details emerge using torus modifications.