A couple of days back, after Sharmila had returned from India, we went out for lunch. We were discussing her experiences in India when the topic went to the new restrictions of driving in New Delhi. If you were not aware, New Delhi has promulgated new rules (I am not sure if it is effective still) that stipulates that cars with odd or even number license plates can be driven on alternate days. So, one day, if cars with only even number license plates can be driven, the next day it would be for the cars with odd number license plates. This, if I am not very mistaken, is to keep the pollution under control.

As a side story, I am told that women drivers are exempt from this rule. Which prompted me to suggest to Sharmila that we lost a great business opportunity to sell “burkhas” (the head to toe garb that many Muslim ladies wear) in New Delhi. Who is going to figure out whether it is a guy or a girl driving once they put a “burkha” on 🙂

In any case, another idea came to mind then. How about those guys with license plates that are reversible? Like if I had a license plate “6666”, I can easily take out four screws and put them back on with the license plate looking “9999”. In practice, that is not possible since there are other things written on the license plate that will clearly expose the trick but that did give rise to today’s puzzle:

How many license plates can be there which when reversed (and reattached to the car) gives a legitimate alternate parity (odd becomes even, even becomes odd) license plate?

Assume the following:

1. License plates are no more than 4 digits long
2. A license plate cannot start with 0
3. 0,1,6,8,9 are the digits that while reversed looks like legitimate digits
4. There cannot be two license plates which look the same on the roads ever

Here you go Debajyoti – since you were clamoring for another one. This one involves probability and can be considered very simple or very intriguing depending on your point of view…

I was having drinks with two of my friends last evening when the discussion meandered around our kids. All three of us have two kids each and no twins. Chris mentioned that his boy has really taken to high school football. The other child is less inclined towards sports and prefers to excel academically. Rick, the other friend – who is the youngest of the three of us – talked about his four year old son overjoyed with his grandparents’ visit during Christmas and all the gifts he got. Rick and his wife also just had a baby – and that was one more reason the grandparents had come – to help them around in the house.

So, now the question for you: Which of my two friends – Chris or Rick is more likely to have a daughter?