Local Quiz

[grumpee]

Can anyone help me with this


In a meeting between the manager and two of his team, Dave and Ann, the manager says that one or both of them have been given a recognition award. He has already privately let each know if the other has received an award but not if they personally received one.

He asks them to say if they themselves have received an award but neither says anything.

He asks them one last time if they themselves have received an award.

Who speaks?
a) Neither b) Dave c)Ann d) both

[grumpee]

Any ideas?

[Fibonacci]

1) do they have to respond ?
2) do they have to answer truthfully ?

[tonyav]

I should think that the answer is neither.

[Tilly2]

If they didn't say anything the first time, why would they say anything the second time?

[grumpee]

Yes I see what you mean - why would they say anything the second time not having said anything the first - will go with neither

[Davemano]

Neither of them need to answer because they have already been told the answer to the question.

[Tilly2]

Did he ask them individually, or together?

[TOMMO33]

It could be any of the options. Neither has been told their own good or bad fortune, so they have no idea whether to say yes or no. Maybe neither speaks, or perhaps Dave or Ann or both might speak, to say 'I don't know' .

[JJ109]

A HUGE IMPORTANT NOTE
They must both be extreme logicians and honest

Both will speak as BOTH had an award.

Dave knows if Anne has an award and Anne knows if Dave has an award. REMEMBER that at least one of them DOES have an award.

If Anne knows that Dave does NOT have an award, she will know that she DOES as aat least one has. Similarly if Dave knows that Anne does NOT have an award, he will know that he does.

Therefore at the first ask if they knew that their rivl had not hd an award they would have worked out that they had an award and owned up. The fact that they did NOT speak at the first ask means that they knew that the rival DID have an award.

Therefore at the second ask they BOTH know they each had an award and BOTH say so

[JJ109]

Apologies for my poor typing - I shall try and put this another way.

Put yourself in the shoes of both Anne and Dave. They each know two facts
1. At least one of them received an award
2. Whether their "colleague" received one or not

If their "colleague" received an award, they wouldn't have a clue whether they themselves had one or not, as one or both could. HOWEVER, if their colleague did not receive an award, it means that they themselves DID receive one, as AT LEAST one of them has to receive one.

Therefore at the first ask IF their colleague did NOT receive an award, Anne or Dave would speak up and admit that they themselves had received one.
The fact that they DID NOT speak, means that they did not know. The only way that they could not know whether they themselves had an award is if their respective colleagues DID receive an award.

They are clever people and work this out. They now both know that they both received an award. Therefore at the second ask, they BOTH answer that they received an award.

[grumpee]

thanks JJ109 - that makes sense

[JJ109]

You're welcome

[TOMMO33]

That's an excellent explanation, but there is nothing to say that they're obliged to speak each time, nor are they both necessarily good logicians. Still, well done.