Cheryl's birthday is a puzzle in logic in which Albert and Bernard determine a date from statements about their knowledge. The possible dates are May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, and August 17. Albert initially receives only the month, and Bernard only the day. Both know the candidates and this allocation of information. Their truthful announcements occur in this order:
1. Albert cannot identify the date, but knows Bernard cannot identify it either.
2. Bernard could not identify it initially, but can after hearing Albert.
3. Albert can now identify it too.
Initially, only the days 18 and 19 occur once, so Albert's certainty about Bernard excludes May and June. Among the remaining dates, only day 14 occurs twice. Bernard's new knowledge excludes July 14 and August 14, leaving July 16, August 15, and August 17. Albert can distinguish July 16 from his month, but cannot distinguish the two August dates. Thus Cheryl's birthday is July 16 (van Ditmarsch et al. 2017, pp. 1 and 3-4).
