PUZZLING UNISEX NAMES

I am no film buff, but I remember the Raj Kapoor film ‘Bobby’ very well. This 1973 Bollywood film was widely popular. Dimple Kapadia debuted in the film playing the daughter of a poor fisherman Jack Braganza (played by Prem Nath). It gave the first leading role to Rishi Kapoor as the son of a rich businessman Mr Nath (played by Pran). Numerous movies in the following years in several languages were inspired by this plot.

It is not for these reasons or because it was a trend-setter which introduced the genre of teenage romance with a rich-vs-poor clash as a backdrop that I remember the movie. There are two very different reasons.

The first of them can be called a story within a story. It needs some elaboration. I saw the movie one Sunday in the Globe Cinema in Calcutta. There was this scene in the film where the mother is busy in the kitchen preparing a meal for the family. She is cutting a big fish when the distraught daughter comes to the kitchen and breaks the news to her mother – that she is expecting. The mother is shocked and turns hysterical; she drops the knife and the fish, as the whole world comes crumbling down.

It is an emotion-charged moment and the audience is tense. From the front row, someone shouts, ‘O maacchh-ta kothey gaye-lo?’ (Loosely translated as: What happened to the fish?) As a Mallu who likes his fish, I could commiserate with the piscophagic Bong brother.

The second is that all along, I had thought only boys were named ‘Bobby’ and this movie proved me wrong. Dimple, the young heroine was ‘Bobby’ here.

In later years, during my stint in Punjab, I had an overdose of unisex names. (Not that Kerala does not have its share: Money, Baby, Joy, Shine, Jolly etc being some.) Amrinder, Parminder and Shivinder could be a Kaur or a Singh.

Thereby hangs a puzzle:

My wife used to teach in a co-ed school in Patiala. She was the class teacher in Class X C of the school. Gurinder and Bhupinder were the Monitor and the Assistant Monitor of the class.

On the first day, she asked Gurinder: How many of you are girls?

Gurinder replied: 5/14 of my classmates are girls.

She repeated the question to Bhupinder.

Bhupinder replied: 3/8 of my classmates are girls.

What are the genders of Gurinder and Bhupinder?

Some may think this is a trick question and others may even dismiss this as having nothing do with mathematics! But if you apply yourself carefully, you can see that if both were girls, their answers would have been identical. Similarly, if both were boys, their answers would have been identical.

The fact that the answers that Gurinder and Bhupinder different makes it clear that they are of different genders.

Compare 5/14 and 3/8. We see that 5/14 = 20/56 and 3/8 = 21/56. Obviously, Gurinder is a girl and Bhupinder is a boy.

If it is not ‘obvious’, and further explanation were needed, it can be inferred that the person who says that the lesser fraction, namely, 20/56 (and not 21/56) of classmates are girls is a girl herself [and the person who says 21/56 (and not 20/56) of classmates are girls is a boy]. Therefore Gurinder is a girl and Bhupinder is a boy.

In case a mathematical solution is required, let the number of boys and girls be b and g respectively.

If Gurinder is a boy and Bhupinder is a girl, Gurinder’s statement means ‘g/(b + g - 1) = 5/14’ and Bhupinder’s statement means ‘(g – 1)/(b + g - 1) = 3/8.Subtracting, 1/(b + g - 1) = 5/14 – 3/8 = ( - ) 1/56 which is not possible. Therefore Gurinder is a girl and and Bhupinder is a boy.

Further research: As Gurinder is a girl and and Bhupinder is a boy, Gurinder’s statement means ‘(g – 1)/(b + g - 1) = 5/14’ and Bhupinder’s statement means ‘g/(b + g - 1) = 3/8.Subtracting, 1/(b + g - 1) = 3/8 – 5/14 = 1/56. This means (b + g) = 57. Substituting in g/(b + g) = 3/8, g/56 = 3/8 or g = 21. Therefore b = 36.

Sanity Check: What Gurinder, a girl, says means !21 - 1)/(57 - 1) = 5/14. What Bhupinder, a boy, says means 21/(57 - 1) = 3/8.