when is cheryl’s birthday?

maths-question

an idiot-friendly solution to cheryl’s birthday…

the first part of albert’s statement — “i don’t know when cheryl’s birthday is” — can be done away with, it is a mere statement of fact.  the second part — “but i know that bernard does not know too” — is the first important deduction albert made.

what month was albert told?

there are only four possible months, and only two possible deductions.

IF may was the month, albert would say, “bernard MAY KNOW” — if bernard was told “19” by cheryl (since there is only one day that has 19 on it, may 19.)

IF june was the month, albert would also say, “bernard MAY KNOW” — if bernard was told “18” by cheryl (since there is only one day that has 18 on it, june 18.)

IF july was the month, albert would say, “bernard DOES NOT KNOW” — if bernard was told “14”, or “16”.  he couldn’t tell because there were two 14s, july 14 and august 14; and two 16s, may 16 and july 16.

IF august was the month, albert would also say, “bernard DOES NOT KNOW” — if bernard was told “14”, “15”, or “17”; since there were two 14s, july 14 and august 14; two 15s, may 15 and august 15; and two 17s, june 17 and august 17.

bernard’s deduction:

bernard now knows from albert’s deduction — “bernard DOES NOT KNOW” — that the month albert was told was either july or august.

albert’s final deduction:

when bernard said, “I NOW KNOW,” albert immediately knew that bernard was told “16” by cheryl.  albert knows that bernard cannot say “I NOW KNOW” if he was told “14” because there are two possible days with 14, july 14 and august 14.

BUT since albert knows (cheryl told him) the month — july — he knows that bernard was not told either “15” or “17” by cheryl, which are the other two possible dates in august, which cheryl could have told bernard.

cheryl’s birthday — july 16.

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