Cheryl’s Birthday Puzzle Answer: July 16 [Solved]

Cheryl’s birthday puzzle answer: July 16. That is the only date that survives all three statements in the conversation. The rest of this post works through the elimination, one statement at a time, so you can see exactly why every other date drops out.

The Puzzle: 10 Dates, Two Clues

Cheryl gives Albert and Bernard a list of 10 possible dates for her birthday. Then she whispers the month to Albert and the day to Bernard. Neither of them hears the other’s clue, and both of them know how the clues were shared.

Month	Possible dates
May	15, 16, 19
June	17, 18
July	14, 16
August	14, 15, 17

Then the two friends talk, in this order:

• Albert: “I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.”
• Bernard: “At first I didn’t know when Cheryl’s birthday was, but I know now.”
• Albert: “Then I also know when Cheryl’s birthday is.”

Two rules make the puzzle work. First, Albert and Bernard are perfect logicians, so every statement is exactly true. Second, each of them reasons not just from his own clue, but from what the other person could possibly know. That second rule does most of the work.

How the Cheryl’s Birthday Puzzle Answer Falls Out, Step by Step

Step 1: Albert’s first line removes May and June

Start with Bernard’s position. If Bernard had been told the day 19, he would know the birthday at once, because 19 appears only once in the list, on May 19. The same holds for 18, which appears only on June 18. Every other day appears at least twice, so Bernard would be unsure.

Now read Albert’s line again. He says he knows Bernard does not know. For that to be certain, Albert’s month must contain no unique day at all. May contains 19, so if Albert had been told May, Bernard might have been told 19 and might already know. June contains 18, so the same problem blocks June.

July and August pass the test. Every day in July (14, 16) and every day in August (14, 15, 17) appears more than once across the full list, so Bernard cannot know yet whichever of those days he holds. Albert’s line therefore tells everyone, including Bernard, that the month is July or August. Five dates remain: July 14, July 16, August 14, August 15, August 17.

Step 2: Bernard’s line removes the 14th

Bernard has heard Albert’s line, so he also knows the month is July or August. He then says he knows the birthday now. Look at his options within those two months. If Bernard had been told 14, he would still face two dates, July 14 and August 14, and he could not choose between them. So his day cannot be 14.

That leaves three dates: July 16, August 15, and August 17. Each of those days appears only once among the surviving dates, which is exactly why Bernard can now be sure.

Step 3: Albert’s final line picks July

Albert has heard Bernard’s line, so he knows the date is one of July 16, August 15, or August 17. He then says he knows the birthday too. If Albert’s month were August, he would still face two dates, August 15 and August 17, and he could not decide. Since he can decide, his month must be July. July holds only one surviving date.

So the birthday is July 16. That is the Cheryl’s birthday puzzle answer, reached without guessing. Here is the full elimination in one view:

Statement	Dates removed	Dates left
Albert: Bernard cannot know yet	May 15, 16, 19; June 17, 18	July 14, 16; August 14, 15, 17
Bernard: now I know	July 14, August 14	July 16; August 15, 17
Albert: now I know too	August 15, 17	July 16

Why July 16 Is the Only Cheryl’s Birthday Puzzle Answer That Works

Test each survivor against the conversation and watch it fail, except one. August 15 fails at the last step: if the birthday were August 15, Albert would hold August, see two surviving August dates, and could not make his final claim. August 17 fails for the same reason. July 16 passes every step: Albert holds July, Bernard holds 16, and each statement is true exactly as spoken.

It also helps to check the dates that fell early. May 19 fails at the first step, because Bernard would have known at once and Albert could never have claimed otherwise. June 18 fails the same way. July 14 and August 14 survive the first two rounds but fail the second statement, because Bernard could not have become sure while holding 14.

The Trap Most Solvers Fall Into

Most people read Albert’s first line as a claim about his own knowledge only: he does not know, and he guesses Bernard does not know either. But the puzzle only works if Albert’s claim is certain. He must be able to rule out every world in which Bernard already knows, and that forces him to rule out any month containing a unique day.

A second trap is stopping after step 2. Three dates remain at that point, and August 15 and August 17 both look plausible. They fall only when you apply Albert’s final line with the same strictness: he must be able to decide, and August leaves him undecided. Work the puzzle as a chain of certainties, not guesses, and the answer drops out on its own.

What the Interviewer Is Testing

This puzzle tests common-knowledge reasoning: thinking about what someone else knows, and what they know about what you know. That skill shows up constantly in finance work, from reading a counterparty’s move to judging what a market has already priced in. The interviewer is not testing speed arithmetic. The Cheryl’s birthday puzzle answer needs almost no arithmetic at all.

It also tests disciplined elimination. Strong candidates write the list down, cross dates out in rounds, and check each surviving date against every statement. Weak candidates jump to a date that feels right and then defend it. If you state your method out loud as you go, the interviewer can follow your logic even before you reach July 16, and that matters as much as the final date.

Finally, the puzzle tests comfort with “I know that you don’t know” statements. Many candidates freeze when a clue is about someone else’s ignorance rather than a fact. Treat each statement as fresh information about the whole list, update the list, and move on.

Try It Yourself: A Mini Version

Try the same machinery on a shorter list before your next practice round. Suppose the possible dates are May 14, May 15, and June 14. Albert knows the month, Bernard knows the day, and Albert opens with the same line: “I don’t know, but I know Bernard doesn’t know either.”

Work it through. The day 15 is unique, so Albert’s line rules out May, which is the only month containing 15. That leaves June 14, so Bernard, holding 14, now knows, and Albert, holding June, knows too. The answer is June 14. If you solved that without peeking, you have the method, and the full Cheryl puzzle is just the same method with a longer list.

Cheryl’s Birthday Puzzle: Quick FAQs

Is July 16 the only possible answer?

Yes, on the puzzle’s own terms. Once you accept that Albert and Bernard reason perfectly and that every statement is true, the elimination leaves exactly one date. Any other date makes at least one of the three statements false.

Why can’t the answer be August 17?

Because Albert’s final claim would fail. With August as his month, he would still face August 15 and August 17 after Bernard’s line, so he could not honestly say he knows. Only July leaves him with a single date.

Where did this puzzle come from?

It appeared in the 2015 Singapore and Asian Schools Math Olympiad, set by Joseph Yeo, and went viral after a Singapore television presenter shared it online. Since then it has become a staple of logic-interview prep lists, which is why it still shows up in practice sets for consulting, banking, and tech interviews.

Try Another Puzzle Next

If you liked working out the Cheryl’s birthday puzzle answer, try the Blue Eyed Islanders Puzzle, where 100 islanders all leave on night 100, or the 100 Prisoners Boxes Puzzle, where a simple chain rule lifts the prisoners’ odds to about 31%.