Cheryl And Betty Celebrate

Logic Level 3

One day, Cheryl and Betty list down possibilities for their birthday dates.

By some strange coincidence, they wrote the same possibilities for their birthday dates.

They were

Jun 4Jun 6Jun 8
Jul 4Jul 5Jul 6Jul 8
Aug 4Aug 5Aug 7Aug 9
Sep 3Sep 5Sep 7Sep 10

Cheryl then told Betty the day of month of her birthday.

Betty told Cheryl the month of her birthday.

Cheryl: "I know that Betty does not know my birthday."

Betty: "Cheryl does not also know my birthday and my birthday is not on Sep 5."

Cheryl: "You gave me redundant information and my birthday is not on Aug 7."

Betty: "Now I know your birthday and the day of the month of my birthday is a prime number."

Cheryl: "Now I know your birthday."

What is the difference (in days) between Betty's and Cheryl's birthday? (both dates inclusive).

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