# Cheryl’s Birthday Problem: Omer Edition

Cheryl’s Birthday Problem: Omer Edition
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Two aliens land in Jerusalem. One is named Shmerel, the other – Berel. “Take us to your chief!” they say. Passersby take them to a local rabbi, a venerable sage with a long white beard.

“Rabbi,” they ask, “what day of the Omer are you counting on Earth?”

The rabbi smiles into his beard and replies: “I won’t tell you what day is today, but I will give you ten possible dates:"

One week and two days to the Omer
One week and three days to the Omer
One week and six days to the Omer
Two weeks and four days to the Omer
Two weeks and five days to the Omer
Three weeks and one day to the Omer
Three weeks and three days to the Omer
Four weeks and one day to the Omer
Four weeks and two days to the Omer
Four weeks and four days to the Omer

Then, he whispers to Shmerl the actual number of weeks, and to Berel the number of days.

Shmerl: “I don’t know today’s Omer, but I know that Berel does not know either.”

Berel: “At first I didn’t know today’s Omer, but I know now.”

Shmerl: “Then I also know today’s Omer.”

So on what day of the Omer did this exchange take place?

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Anonymous May 16, 2016

Fun one! Thanks for posting! Reply

josy perugia April 17, 2015

2 weeks and five days Reply

R. May 5, 2017
in response to josy:

That can't be, because there is only one 5 day of the Omer, so Berel would obviously know the date. So the 2 weeks are rules out cuz Shmerel wouldn't know which Berel had. Using the same logic, at the 1 weeks are rules out, b/c there is only one 6, and Shmerel wouldn't know that Berel couldn't have known. Now the 3, 2, and 4 days of the 3 and 4 weeks have to be ruled out b/c Berel ruled out the previous ones based on the above. Then all that's left is 3 weeks and 1 day and 4 weeks and 1 day. The only one that makes sense is 3 weeks and 1 day bc there are only 2 of the 3 weeks and 3 of the 4 weeks. Reply

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