This is the finalpart of the solution for the problem which I provided a few days ago. If you have not read this then please start from the first part of this problem – When is Cheryl’s birthday.

Yesterday I provided the second hint to you, and we concluded with the following:

blockquote>STATEMENT 3: Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Bernard is able to tell which is the correct date simple from what Albert said in STATEMENT 1. So how could he deduce this?

Well we already know that the month must be July or August, since from STATEMENT 2 Albert KNOWS that Bernard DOES NOT KNOW and thus the day cannot be 18 or 19.

So STATEMENT 2, which is from Bernard, is following form Albert’s STATEMENT 2. Albert knows the day of the month, and there are two months left with July having two possible dates, and August having three.

July 14      July 16
August 14    August 15     August 17

Bernard previously did not know, but knowing what Albert has said Bernard has been able to deduce that the months must be one of July or August. Now he indicates that he KNOWS, and can only be certain if he has been given a day which is sufficient to deduce that this is unique. This makes the options 16, 15, or 17. 14 will not count since there are two options. However, since he claimed he KNOWS this must be July 16, which has only a choice of two options.

STATEMENT 4: Albert: Then I also know when Cheryl’s birthday is.

Now Albert KNOWS that Bernard KNOWS the right birthday, and this can only be July 16, since even though he does not know the day of the month, the only way that Bernard will KNOW for certain is if there is only one possible option, which only occurs with July 16.

July 14 and August 14 can be eliminated becuase there is no way to determine which of the two would be the right date if the day was 14.

August 15 and 17 can be eliminated since if it was one of these, then he could not be certain which day Bernard actually had.

In summary, this is a very challenging problem, and this is more logic then mathematics, using the powers of deduction, trial-and-error, and elimination, to find the combination of KNOWs and DON’T KNOWs which meet these statements.

This is quite similar to the kind of deductions you need to conduct during the game of Cluedo, which would be a great way to learn how to perform such logical calculations, as distinct from mathematical and arithmetical calculations.

If you have similar types of problems, then please send them through to my by email, and I will see how we can incorporate them into our posts in the future.
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