Cheryl's Birthday Problem Part 2: Singapore viral

Cheryl's Age

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 what is Cheryl's age?

This question was uploaded by Nanyang Technological University on the Facebook and the sequel of the  most viral problem of Singapore known as Cheryl's Birthday.

This child Cheryl is really smart &  always plays games with Albert & Bernard.

So if you're not able to guess Cheryl's age check the solutions below.

Sol. Below

line 1:

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. 

Line 2:

Albert: We still don't know your age. What other hints can you give us? 

Possibilities of  their age.

Line 3:



Albert x Bernard x Cheryl ( Sum/ Bus number)

1 x 1 x 144  ( 146)

1 x 2 x  72    (75)

1 x 3 x  48    (52)

1 x 4 x 36    (41)

1 x 6 x 24    (31)

1 x 8 x 18    (27)

1 x 9 x 16    (26)

1 x 12 x 12  (25)

2 x 2 x 36    (40)

2 x 3 x 24    (29)

2 x 4 x 18    (24)

2 x 6 x 12    (20)

2 x 8 x 9      (19)

3 x 3 x 16   (22)

3 x 4 x 12   (19)

3 x 6 x 8     (17)

4 x 4 x 9     (17)

4 x 6 x 6     (16)

Line 4 :

 Bernard :Of course we know the bus number, but we still don't know your age. 

Here Bernard said that he  knows the bus number ,this line is not helpful ;
 but he also added that they don't know his age it is only possible if the sum is 17 & 19. As both these sum are repeating twice :

3 x 6 x 8 (17)

4 x 4 x 9 (17)

2 x 8 x 9 (19)

3 x 4 x 12 (19)

Other than these two , all sum are unique.

Line 5: 

Cheryl: Oh, I forgot to tell you that my brothers have the same age. 

Here Cheryl said that his both brothers have same age.

3 x 6 x 8 (17)

4 x 4 x 9 (17)

2 x 8 x 9 (19)

3 x 4 x 12 (19) 

From above there is only one possibility with this condition i.e. 4 x 4 x 9.

So the Cheryl's age is 9 yrs.

Ans : 9

Source : Wikipedia