Viral logic problem converted for LRC

Non-Running Pop Culture

9 years ago 04/17/2015 9:28am EDT

A good way to kill a few minutes. This viral logic problem has been converted from figuring out Cheryl's birthday to figuring out her 5K PR. Have fun!!

Albert and Bernard just met Cheryl. “What’s your 5K PR?” Albert asked Cheryl.

Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 times:

16:30, 16:45, 16:54

17:47, 17:52

18:25, 18:45

19:25, 19:30, 19:47

“My 5K PR is one of these,” she said.

Then Cheryl whispered in Albert’s ear the # of minutes — and only the # of minutes — of her 5K PR. To Bernard, she whispered the # of seconds - and only the # of seconds – of her 5K PR.

“Can you figure it out now?” she asked Albert.

Albert: I don’t know what your 5K PR is, but I know Bernard doesn’t know, either.

Bernard: I didn’t know originally, but now I do.

Albert: Well, now I know, too!

What is Cheryl’s 5K PR?

9 years ago 04/17/2015 9:45am EDT

re: brodjoe

brodjoe wrote:
A good way to kill a few minutes. This viral logic problem has been converted from figuring out Cheryl's birthday to figuring out her 5K PR. Have fun!!
Albert and Bernard just met Cheryl. “What’s your 5K PR?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 times:
16:30, 16:45, 16:54
17:47, 17:52
18:25, 18:45
19:25, 19:30, 19:47
“My 5K PR is one of these,” she said.
Then Cheryl whispered in Albert’s ear the # of minutes — and only the # of minutes — of her 5K PR. To Bernard, she whispered the # of seconds - and only the # of seconds – of her 5K PR.
“Can you figure it out now?” she asked Albert.
Albert: I don’t know what your 5K PR is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!
What is Cheryl’s 5K PR?

16:54

9 years ago 04/17/2015 9:47am EDT

re: brodjoe

Who cares, Cheryl is a hobbyjogger.

9 years ago 04/17/2015 9:47am EDT

re: brodjoe

9 years ago 04/17/2015 9:52am EDT

re: brodjoe

9 years ago 04/17/2015 10:16am EDT

re: Lenny Leonard

Lenny Leonard wrote:
18:45

Agreed.

9 years ago 04/17/2015 10:18am EDT

re: brodjoe

9 years ago 04/17/2015 11:11am EDT

re: brodjoe

So Bernhardt learns that Albert was told a non-unique number AND Bernhardt learns that bis number was not unique to a minute?

But he figures it out right away?

Then it's 17:47, isn't it?

9 years ago 04/17/2015 11:23am EDT

re: IG SC feed b

If Albert was told 17, then he could not say that he is sure that Bernard does not know the PR. The ':52' option would give Bernard the full time.

Therefore, the time cannot start with 17. The same logic applies to any time starting in 16 (Because of 16:54).

9 years ago 04/17/2015 2:38pm EDT

re: brodjoe

brodjoe wrote:
A good way to kill a few minutes. This viral logic problem has been converted from figuring out Cheryl's birthday to figuring out her 5K PR. Have fun!!
Albert and Bernard just met Cheryl. “What’s your 5K PR?” Albert asked Cheryl.
Cheryl thought a second and said, “I’m not going to tell you, but I’ll give you some clues.” She wrote down a list of 10 times:
16:30, 16:45, 16:54
17:47, 17:52
18:25, 18:45
19:25, 19:30, 19:47
“My 5K PR is one of these,” she said.
Then Cheryl whispered in Albert’s ear the # of minutes — and only the # of minutes — of her 5K PR. To Bernard, she whispered the # of seconds - and only the # of seconds – of her 5K PR.
“Can you figure it out now?” she asked Albert.
Albert: I don’t know what your 5K PR is, but I know Bernard doesn’t know, either.
Bernard: I didn’t know originally, but now I do.
Albert: Well, now I know, too!
What is Cheryl’s 5K PR?

Because Albert says he knows Bernard doesn’t know, that means the time has to have a seconds value that occurs more than once. Thus, 16:54 and 17:52 can be crossed out.

Since Albert knows that Bernard doesn’t know, we know that the minutes amount includes only times with duplicate second amounts, because if he heard the minute amount 16 or 17 that would mean there was a chance that Bernard heard one of the unique second amounts, meaning he would know. So we can cross out all of the times starting in 16 or 17.

Since Bernard says he now knows, that means it’s not 18:25 or 19:25 because there’d be no way for him to know which of those it was, and it’s also not 19:30 or 19:47 because there’d be no way for him to rule them out either. So Cheryl’s PR is 18:45.

9 years ago 04/17/2015 2:41pm EDT

re: brodjoe

That wall of inane text made my eyes cross, sorry, you lose.

9 years ago 04/17/2015 2:43pm EDT

re: yuppers

yuppers wrote:
Lenny Leonard wrote:
18:45
Agreed.

This. Has overlaps on both minutes and seconds.

9 years ago 04/17/2015 3:06pm EDT

re: brodjoe

There are only 2-4 females on LetsRun, all with PB's in the mid-high 18's. Only one of them likes logic puzzles. Obviously she would re-cast the riddle from her own perspective. I believe her PB is around 18:45 so that is my final answer. Am I right?

9 years ago 04/17/2015 11:47pm EDT

re: LRC Puzzle Solver

Recently a math teacher that I know posted this on facebook lamenting his inability to figure it out... Of course this is something that is covered in a first year logic class. I remember having this problem as a freshman in college.

Nevertheless people just run around the words of the problem and get all in a tizzy, rather than simply dissecting the information behind the words. There is information to be had even in the lack of information.

9 years ago 04/18/2015 1:08am EDT

re: brodjoe

19:47. If my friend Al is so sure.

9 years ago 04/18/2015 3:16am EDT

re: brodjoe

Doper.

It's 18:45, but she's clearly worth 16.23-24.low.

9 years ago 04/18/2015 4:05am EDT

re: brodjoe

Albert: IDN + BerDN => - (16 or 17)

Bernard: NIN => - (18:25 or 19:25)

Albert: NIN => - (19:30 or 19:47)

=> 18:45

9 years ago 04/18/2015 5:28am EDT

re: brodjoe

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