Are you smarter than 15 year olds ?
When is Cheryl Birthday – Brain Teaser of the Day

When we first stumble on this SASMO (Singapore and Asian Schools Math
Olympiad) question for 15 year olds, we stared and re-read the question
a few times, scratching our head as to how to find out Cheryl’s birthday
with such minimal information. After struggling for a few minutes, we
finally manage to figure out the answer by logical elimination.

Question :

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

May 15           May 16             May 19
June 17           June 18
July 14            July 16
August 14      August 15        August 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 does not know too.
Bernard: At first I don’t 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 ?

[ Try your Best before Scroll down for the answer  ]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Brain Teaser of the Day Answer :

Cheryl’s birthday is July 16.

So how can we derive the answer logically ?

Let’s dissect the information provided,

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

From the above statement, we now know that

1) Albert knows Cheryl’s birthday month.
2) Bernard knows Cheryl’s day of birthday.

Next statement,
“Albert: I don’t know when Cheryl’s birthday is, but I know that
Bernard does not know too.”

Since Bernard knows Cheryl’s day of birthday, in order for
Bernard not able to determine Cheryl’s birthday out of the
10 possible dates provided, the day must not be unique.

July 14, August 14
May 15, August 15
May 16, July 16
June 17, August 17
June 18 <– Eliminated
May 19 <– Eliminated

Hence, we can eliminate June 18 and May 19.

Next statement,
“Bernard: At first I don’t know when Cheryl’s birthday is, but I
know now.”

After Bernard knows that Albert and himself does not know
when Cheryl’s birthday is despite Albert knowing Cheryl’s
birthday month and Bernard knowing Cheryl’s day of birthday,
Bernard does his own logical elimination.

Bernard thinking to himself :

1) “In order for both Albert and myself not able to determine
Cheryl’s birthday, Cheryl must have told Albert her birthday
month is either July or August.”

2) “If Cheryl had told Albert her birthday month is either
May or June, then it is possible that I may know Cheryl’s birthday
may be June 18 or May 19. Since Albert has confirmed that both
of us do not know Cheryl’s birthday, then May or June is out”

3) “Hence, we are left with July 14, July 16, August 14, August 15, August 17”

May 15, May 16, May 19 <– Eliminated
June 17, June 18 <– Eliminated
July 14, July 16
August 14, August 15, August 17

4) “Of the remaining 5 possible dates, July 14 and August 14 can
be eliminated.”

If Cheryl’s birthday is either of the 2 dates, then Bernard would not
know Cheryl’s birthday as both dates are 14.

Hence, 3 possible dates remains, July 16, August 15, August 17. Since
Bernard knows Cheryl’s day of birthday, he thus knows Cheryl’s birthday.

Last statement,
“Albert: Then I also know when Cheryl’s birthday is.”

With this last statement, we know that Cheryl’s birthday is July 16.

If Cheryl told Albert her birthday month is August, then Albert would not know
when exactly Cheryl’s birthday is as there are 2 possibilities (August 15 or August 17).
Hence, Cheryl must have told Albert her birthday month is July.   🙂

Leave a comment below if you manage to solve this brain teaser of the day.

 

The following brain teasers are challenging and requires considerable amount
of brain juice. Can you solve all of them ?