Cheryl's Birthday facts for kids

Cheryl's Birthday is a super cool logic puzzle! It's like a brain-teaser where you use clues to figure something out. Dr. Joseph Yeo Boon Woi from Singapore created this puzzle. The main goal is to find out when a girl named Cheryl has her birthday. She gives some hints to her friends, Albert and Bernard.

This puzzle was part of the Singapore and Asian Schools Math Olympiad (SASMO) in 2015. A TV presenter from Singapore, Kenneth Kong, first shared it online. It quickly became super popular, spreading like wildfire in just a few days!

How the Puzzle Became Famous

The "Cheryl's Birthday" puzzle first appeared on Facebook. Kenneth Kong, a TV presenter in Singapore, posted it on April 10, 2015. It quickly went viral, meaning lots of people shared and talked about it.

Kong posted the puzzle after discussing it with his wife. He thought it was for younger kids, around 10 or 11 years old. But it was actually from the 2015 Singapore and Asian Schools Math Olympiad. This competition was for students around 14 years old. Kong later realized his mistake.

The math competition happened on April 8, 2015. About 28,000 students from Singapore, Thailand, Vietnam, China, and the UK took part. The people who organized SASMO said the puzzle was for the top students. It was designed to "sift out the better students," meaning it helped find the really smart ones. The executive director of SASMO told the BBC that logical thinking is important in daily life and at work.

The Birthday Puzzle Itself

This puzzle was question number 24 out of 25 questions in the competition. Here's what it said:

Albert and Bernard just become [sic] friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

May		15	16			19
June				17	18
July	14		16
August	14	15		17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too. [sic]
Bernard: At first I don't [sic] know when Cheryl's birthday is, but I know now.
Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?

Solving Cheryl's Birthday Puzzle

The correct answer to the puzzle is July 16.

You can solve this puzzle by slowly removing dates that don't fit the clues. Here's how Alex Bellos from The Guardian newspaper explained it:

Step 1: Albert's First Clue

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too.

Albert only knows the month. Since every month has more than one possible date, of course he doesn't know the exact birthday. That first part of his sentence is just extra information.

Now, think about Bernard. Bernard knows only the day. He could only know the exact birthday right away if his day number appeared only once on the list. Looking at the list, the numbers that appear only once are 18 (June 18) and 19 (May 19).

For Albert to know that Bernard doesn't know, Albert must have a month that does NOT include 18 or 19. This means Albert must have been told July or August. If Albert had May or June, Bernard could have known (if he had 18 or 19). So, we can cross out all May and June dates except for those that are not 18 or 19.

• May: 15, 16, 19 (19 is out)
• June: 17, 18 (18 is out)

So, the possible dates are now:

• May: 15, 16
• June: 17
• July: 14, 16
• August: 14, 15, 17

But wait! Albert knows Bernard doesn't know. This means Albert's month can't contain a unique day like 18 or 19. So, if Albert knows the month is May, he would think Bernard might know if the day was 19. Same for June and 18. So, Albert knowing Bernard doesn't know means the month must be July or August. This eliminates all May and June dates entirely.

New possible dates:

• July: 14, 16
• August: 14, 15, 17

Step 2: Bernard's Clue

Bernard: At first I don't know when Cheryl's birthday is, but now I know.

Bernard now knows that Albert's month is either July or August. If Bernard now knows the full date, his day number must be unique within the remaining July/August dates.

Let's look at the remaining days: 14, 15, 16, 17.

• If Bernard had been told "14", he wouldn't know if it was July 14 or August 14. So, 14 is out.
• If Bernard had been told "15", he would know it's August 15 (because July 15 is not an option).
• If Bernard had been told "16", he would know it's July 16 (because August 16 is not an option).
• If Bernard had been told "17", he would know it's August 17 (because July 17 is not an option).

So, Bernard must have been told 15, 16, or 17. This means the date cannot be July 14 or August 14.

New possible dates:

• July: 16
• August: 15, 17

Step 3: Albert's Final Clue

Albert: Then I also know when Cheryl's birthday is.

Albert now knows the possible dates are July 16, August 15, and August 17. For Albert to now know the exact birthday, his month must be the one with only one option left.

• If Albert had been told August, he would still have two choices: August 15 or August 17. He wouldn't know for sure.
• If Albert had been told July, he would know for sure: July 16.

Therefore, Albert must have been told July. This means the birthday is July 16.

Why Some Other Answers Are Wrong

After the puzzle became famous, some people thought the answer was August 17. However, the SASMO organizers said this was incorrect.

These wrong solutions often miss a key part of Albert's first statement: "I know that Bernard doesn't know too." This part gives Bernard important information. Bernard knows that Albert could only say this if Albert's month did not contain the unique days (18 or 19). This means Albert's month had to be July or August. Once Bernard realizes this, he can rule out May and June. This allows him to figure out the birthday even if his day was 15 or 16, not just 17.

The SASMO organizers explained that August 17 would be the answer if the conversation started differently. For example, if Bernard said he didn't know first, or if Cheryl herself said Bernard didn't know. But with the original conversation, July 16 is the only correct answer.

Cheryl's Age: A Second Puzzle

On May 14, 2015, Nanyang Technological University shared a second puzzle on Facebook. It was called "Cheryl's Age."

Here's the puzzle:

Albert and Bernard now want to know how old Cheryl is.

Cheryl: I have two younger brothers. The product of all our ages (i.e. my age and the ages of my two brothers) is 144, assuming that we use whole numbers for our ages.
Albert: We still don't know your age. What other hints can you give us?
Cheryl: The sum of all our ages is the bus number of this bus that we are on.
Bernard: Of course we know the bus number, but we still don't know your age.
Cheryl: Oh, I forgot to tell you that my brothers have the same age.

Albert and Bernard: Oh, now we know your age.

So, how old is Cheryl?

Solving Cheryl's Age Puzzle

First, Cheryl says she is the oldest of three siblings. Their ages, when multiplied together, equal 144. We need to find all the ways to multiply three whole numbers to get 144. For example, 16 x 9 x 1 = 144, or 8 x 6 x 3 = 144.

Next, Cheryl says the sum of their ages is the bus number. Bernard knows the bus number, but he still can't figure out Cheryl's age. This means the sum of the ages must be a number that can be made in more than one way. When you list all the possible age combinations that multiply to 144, you find two sums that appear more than once:

• 9, 4, 4 (sums to 17)
• 8, 6, 3 (sums to 17)
• 12, 4, 3 (sums to 19)
• 9, 8, 2 (sums to 19)

Since Bernard knows the bus number (the sum) but still can't tell Cheryl's age, the sum must be 17 or 19. If the sum was any other number, there would only be one set of ages, and Bernard would know.

Finally, Cheryl says her brothers are the same age. This clue helps Albert and Bernard figure it out!

• If the sum is 17, the options are (9, 4, 4) or (8, 6, 3). Only (9, 4, 4) has brothers with the same age.
• If the sum is 19, the options are (12, 4, 3) or (9, 8, 2). Neither of these has brothers with the same age.

So, the only possibility left is 9, 4, 4. This means Cheryl is 9 years old, and her two brothers are both 4 years old. The bus number they are on is 17.

Denise's Revenge: A Third Puzzle

On May 25, 2015, Alex Bellos, a math writer, shared another puzzle. It was called "Denise's Revenge" and was also written by Dr. Yeo, who created the first puzzle. This one introduces a new character, Denise, and Albert, Bernard, and Cheryl try to find her birthday.

The puzzle gives a list of 20 possible dates for Denise's birthday. Then, Denise tells Albert the month, Bernard the day, and Cheryl the year of her birthday, all separately. A conversation follows, similar to the first puzzle, with each person giving clues.

The solution to "Denise's Revenge" was published the next day. It's solved the same way as "Cheryl's Birthday," by carefully eliminating dates with each new clue. The correct answer is 14 May 2002.