Puzzle: Inverted License Plates (or why Sharmila does not go for lunch with me anymore :-) )
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:
- License plates are no more than 4 digits long
- A license plate cannot start with 0
- 0,1,6,8,9 are the digits that while reversed looks like legitimate digits
- There cannot be two license plates which look the same on the roads ever
This wont work in Indian metros :-). We use a HSNP here, which are rivetted, not screwed. Every time you open the plate, you need a new one.
What is HSNP?
High security number plate.
😀
Isnt that the best way to say “I dont know?”
🙂
For me, I am saying
Bijit, Pratyush and Sanjib, the discussion so far has been errr… “rivetting” 🙂 Now solve the problem 🙂
well, I thought that with all this brouhaha, you would withdraw the puzzle 😛
Does this look correct…?
Ummm… No.
It should be much more than that
Thanks for your encouragement – I am sure that will push me to know you more Sanjib. Now let us give the control back to Rajib as far as this post is concerned.
Will make an attempt to solve this as soon as I head out for lunch.
Sanjib, you must have become very hungry by now? 🙂
You won’t believe what I did. My car key is inside the trunk along with my stuffs and I’m 24 miles away to catch my flight to Atlanta in next 75 mins. Waiting for AAA/Avis to give me some solution unless you’ve one!
100
Nitin, how did you get 100?
4*5*5*4=400. Can’t start with 0, So can’t end with 0
First digit can have 4 numbers, second digit can have 5 numbers, third digit can have 5 numbers and the last digit can have only 1 number (6 or 9 , because of your last requirement). 4 times 5 times 5 times 1 = 100
Jay, the last digit cant take 0, 1 or 8, since reversing those does not change odd to even. It can only take 6 or 9, and not both because of the last requirement
When you said reversing, I was thinking upside down. If you mean reversing left to right, my argument is not valid
I did miss 6 & 9 (upside down), so it should be 4*5*5*3=300
Nitin to get past “reversing” definition, think about a license plate and how you would put it inverted. Write the number on a paper and turn is upside down. Also, you can have license plates of three digits, two digits etc.
Jay, are you not going to have duplicates? Remember the rule you cannot have two cars with the same plates on the same day.
I assumed all the digits need to be unique within the license plate… If that is not a restriction, then it is 200
Amitabh, Try with just digit license plates – your approach would be 8. However there are duplicates there.