Someone with a Masters degree in reasoning and logic please help me

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#1283155 14-Apr-2015 19:24

I love math olympiads! I remember doing it when I was 10!

Saw this earlier and just by looking at the pattern you can narrow it down to July 15, Aug 16 and Aug 17.

Then you can exclude August 16/17 because if it is august, then both will know at the same time.

Behodar

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#1283159 14-Apr-2015 19:33

joker97: because otherwise Bernard will know the date just by looking at the list, but he could not, so it can't be the 19th or 18th as they are standalone dates

You've lost me. If Bernard only knows the day then how on earth can he work out the month just by looking at the list?

NonprayingMantis

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#1283165 14-Apr-2015 19:39

kendo:
NonprayingMantis: think about the reverse logic and the list of potential answers.

If Albert states he doesn't know, but that he also knows that Bernard doesn't know, then that narrows down the list for Bernard to consider

say, for example, the date was 19th May. If bernard had been told "it's the19th", then he would know the answer was 19th May.
So for Albert, who only knows the month, to confidently state Bernard doesn't know, Albert MUST know the month is one of the months that doesn't contain a unique number. (if it wasn't, he couldn't be sure Bernard didn't know) therefore it can't be June or May. and so must be July or August.
Why cant it be June or May? It cant be the 2 unique dates sure, but how can he be sure that its not one of the other dates in those months that are shared with other months?

Imagine for a moment that it was, say May 16th.
Bernard would be told "16th"
Albert would be told "May"

If Albert was told "May" then (remembering that he doesn't know the actual date) he can't be sure that Bernard won't know the whole answer.

Since he says "I know Bernard doesn't know" the only way for him to know that is for the date to be in a month where there are no unique dates. Otherwise he could only say something like "I don't know whether Bernard knows or not"

Here is another version of the puzzle I just made up along with explanations.

(exact same setup, same date options etc.)

But instead of the statements given we start with:

Albert: "Bernard might know the answer"
Explanation: The only way for this to be possible is if the month Albert was told is one that has a unique date in it - May and June. If it was a month that contained no unique dates, then Bernard definitely would not know the answer.

Bernard: "I didn't know the answer, but now I do."

Explanation: This is two statements. 1) I didn't know the answer straight away 2) now I have heard Albert's statement I do know the answer
For Bernard to have not known before, we know it isn't one of the unique dates (18th and 19th) or his first statement would be false. But now that he has heard Alberts statement, he has narrowed it down to May and June.
So there are three potential options left. May 15th, May 16th, June 17th. Since these are all unique, he must know the correct month.

Albert: "Now I also know the answer"

Albert knows the month already, but not the date. The only way he can know the true answer now is if the month is June. If it was May, he wouldn't know whether it was May 15th or 16th (i.e. if it was either May 15th or 16th, Albert would not know the answer from the information given)

So the answer (in this version) is June 17th

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#1283173 14-Apr-2015 19:40

kendo:
NonprayingMantis: think about the reverse logic and the list of potential answers.

If Albert states he doesn't know, but that he also knows that Bernard doesn't know, then that narrows down the list for Bernard to consider

say, for example, the date was 19th May. If bernard had been told "it's the19th", then he would know the answer was 19th May.
So for Albert, who only knows the month, to confidently state Bernard doesn't know, Albert MUST know the month is one of the months that doesn't contain a unique number. (if it wasn't, he couldn't be sure Bernard didn't know) therefore it can't be June or May. and so must be July or August.
Why cant it be June or May? It cant be the 2 unique dates sure, but how can he be sure that its not one of the other dates in those months that are shared with other months?

ah darn ... i got it before, but now i can't. all the blood is digesting the dinner

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#1283175 14-Apr-2015 19:41

Behodar:
joker97: because otherwise Bernard will know the date just by looking at the list, but he could not, so it can't be the 19th or 18th as they are standalone dates

You've lost me. If Bernard only knows the day then how on earth can he work out the month just by looking at the list?

if Bernard was told "19th". looking at the list it's May 19th.
If Bernard was told "18th". looking at the list it must be June 18th.

NonprayingMantis

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#1283176 14-Apr-2015 19:42

Behodar:
joker97: because otherwise Bernard will know the date just by looking at the list, but he could not, so it can't be the 19th or 18th as they are standalone dates

You've lost me. If Bernard only knows the day then how on earth can he work out the month just by looking at the list?

if the date only appears once in the list (e.g. 19th), then Bernard would know the whole answer just by being given the date. i.e. the only option for the 19th is May 19th.
Because he states "I didn't know the answer before", we know that it must not be one of these unique dates

Rickles

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#1283178 14-Apr-2015 19:44

People keep saying "unique dates" ... what defines a unique date?

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NonprayingMantis

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#1283181 14-Apr-2015 19:48

Rickles: People keep saying "unique dates" ... what defines a unique date?

unique = only appears once in the list.
Remember that Bernard ONLY knows that date number, not the month. at the start.
Albert is told ONLY the month
Bernard is told ONLY the date of the month, but not the month

So if Bernard was told a date number that appears only once in the list (e.g. 18th or 19th) then he would know the final answer immediately. If he was told a number that appears more than once (e.g. 14th appears twice - July and August), he wouldn't immediately know the whole answer.
Therefore, for Albert to confidently state "I know Bernard doesn't know" then the answer can only be in a month without a unique date, otherwise Albert (who only knows the month) could not state that.

Detruire

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#1283183 14-Apr-2015 19:50

Rickles: People keep saying "unique dates" ... what defines a unique date?

In this case, it's a date with a day number that isn't in any of the other dates (e.g. May 19.)

rm *

Behodar

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#1283184 14-Apr-2015 19:51

I can kind of see what you all are getting at, but I can only conclude that all three of them are politicians since they apparently can't use plain facts and instead rely on pointless intrigue. That, and I can't concentrate with my phone going "bing" every 20 seconds as you all reply to the thread...

Rickles

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#1283187 14-Apr-2015 19:53

Nonpraying mantis ... OK, got that, and assumed that to logically be the case, BUT there are also non-unique dates over several months.

I must be missing something here

NonprayingMantis

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#1283190 14-Apr-2015 19:58

Behodar: I can kind of see what you all are getting at, but I can only
conclude that all three of them are politicians since they apparently can't use plain facts and instead rely on pointless intrigue.

everything they state is 100% plain fact. :P

NonprayingMantis

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#1283192 14-Apr-2015 20:02

Rickles: Nonpraying mantis ... OK, got that, and assumed that to logically be the case, BUT there are also non-unique dates over several months.

I must be missing something here

correct, but if the answer was in a month that contains a unique day number then, no matter which date it actually is, then Albert cannot be certain that Bernard doesn't know. (because he only knows the month, not that date)

e.g. if Albert was told "May" then he knows it could be either 15th 16th or 19th. Since he doesn't know which one it is, then he cannot state "Bernard doesn't know the answer" because there is a chance Bernard does know the answer.

so the only months where Albert can definitely state "Bernard does not know" are months that contain no unique day numbers.

Rickles

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#1283205 14-Apr-2015 20:22

>so the only months where Albert can definitely state "Bernard does not know" are months that contain no unique day numbers.<

Agreed, but I am at loss to see how any of the remaining months/dates may be also eliminated.

Kim587

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#1283207 14-Apr-2015 20:27

Rickles: >so the only months where Albert can definitely state "Bernard does not know" are months that contain no unique day numbers.<

Agreed, but I am at loss to see how any of the remaining months/dates may be also eliminated.

So May and June are gone since they have these 'unique' dates in them.

14 can be eliminated because if it was the 14th, Bernard could not have known whether it was july or august.
That leaves July 16, August 15 and August 17 as possible dates.
It therefore must be July 16, because if it was in August Albert would still not be able to tell whether it was the 15th or 17th.

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