Code 4 Bill

Fibonacci system

sriram — Tue, 20 Dec 2005 15:50:00 GMT

We typically learn binary system, hex system in our courses. Most of them are predictable in their position values or they are linear. This system is not linear as its dependant on Fibonacci series.

3 is the first duplicate (ignoring 1 as we started with 1). We can represent 3 as 100 or as 011.From there you have many duplicate representations. There are some numbers which can be represented only one way.

If you find that sequence please let me know. Those numbers are also interesting

- Perraju

Two digit numbers

sriram — Sun, 18 Dec 2005 17:35:00 GMT

I always wondered how to place digits 0 to 9 in a matrix which contains all the digits from 00 to 99 and what is the minimum matrix size that is needed.In this question we are trying to enumerate the number of numbers we can produce. Lot of people are thinking as to the number or rows, columns they would need and then summing them up.

That may not scale that well if we want to find all three digit numbers (not necessarily in sequence means first two digits in a row and third one diagonal).In a MxN matrix, 4 corners and first row, last row, first column and last column are interesting. The rest always has 8 neighbors.

Interesting to see what is the minimum M x N that can hold all numbers from 00 to 99.

Thanks
Perraju

Counting bits - continued

sriram — Sun, 18 Dec 2005 17:32:00 GMT

Lot of people sent code with counting bits method. Some people also sent the permutations sequence and expressions to say how many numbers exist before N that have same 1's in binary form.

Counting 1's in a number is better than O(N) algorithm where N is number of bits in the system. if we use the operators and machine instructions properly it can be with constant instruction (of course there are machine instructions which may be using all the bits of the number)

Example - take a two digit number of binary which is 2X + Y form, if you right shift it becomes X, now if I subtract second one from first we are left with X + Y (number of 1’s in the number)

All we need to do is make sure the place holders can hold the SUM values (if not break the problem) and find an efficient way to add them across different bit sizes (there are some divisors which can pass on the effective sum as they keep on adding the reminder at each stage)

Distinct number of SWAPS as we discussed earlier is a alternative column of Pascal triangle. Number of 1's (1 one's, 2 ones etc) are permutations problem. If we try to create a two dimensional table for each NUMBER of 1's relation to number of SWAPS there is one more pattern which is quite interesting.

Hope some one will crack that.

Thanks
- Perraju

Number of 1s problem

sriram — Sun, 18 Dec 2005 17:29:00 GMT

Previously I asked a question regarding the distribution of how many swaps are needed to move array elements. Here we are trying to count the number of 1's. Counting number of 1's vs the distribution table (All numbers which have 2 1's and how many times they contribute to 0'swap, 1'swap and 2swap) was my interest.

On one hand this problem is a permutations problem. But the fun is if you write a "count number of 1's" code which is less than O(N) complexity where N is number of bits.

- Perraju

December 13th brain teaser

sriram — Wed, 14 Dec 2005 10:49:00 GMT

[ Go to http://www.microsoft.com/india/code4bill/SampleQuestion.aspx to see the question - Sriram]

Trying to move to coding related questions from number sequences. The reason I chose 32 is to make sure recursion doesn’t terminate quickly.Not trying to discourage recursion but real code for this shouldn’t take much time. So performance vs simple code is what matters here.

Some one wrote to me that the program didn’t finish executing after 30mts. May be that’s not the way you should code for this.My program for this comes out in 8.93sec real (on KSH of Interix subsystem) for input 32.

Happy coding. I Will come back to numbers in few days.

- Perraju

The power of 2! (Dec 12th Brain teaser)

sriram — Tue, 13 Dec 2005 09:22:00 GMT

[ To see the question referred to in this blog post, check out www.code4bill.com (the Dec 12th brain teaser) - Sriram Krishnan]

The previous two questions were easy to crack by writing simple code. So I thought we could use some machine power to actually infer the big number.The reason I picked 1048576 is due to it being the first 7 digit number in the POWER series of two ( 2**1, 2**2,...).

I really am not expecting you to code to generate this final number. Observer the power series and crack it.

- Perraju

Oh My God!

sriram — Sun, 11 Dec 2005 13:27:00 GMT

I'm sure several people had had this experience. You spend a lazy Saturday at home whiling away your time and sleeping. Sunday morning, you come to work, open your email and you go 'Oh My God!' at something you see in your email and you curse yourself for not checking your mail the previous day.

Well, I spent all of yesterday away from the computer. This morning, I check my email and my eyes almost popped out at the reaction to Code4Bill. The sheer volume of response from students is stunning - thank you!

More than the fact that there is a New York Times article, more than the fact that there is a Cnet article, the fact that I'm most happy about is that we've been Slashdotted! This was my secret geek dream which has finally come true! Unfortunately, by the time I went to the page, the conversation had died down - otherwise I could have jumped in and taken part.

I said I'll answer questions tommorow - but I can't help but answer 2 questions.

- Where do I sign up?

Head on over to www.code4bill.com . Contest registrations open only on Jan 1st - however, you can give us your email id and we'll send you brainteasers,etc and inform you when registrations open.

- Is there really a Bill Gates technical assistant team?

I saw this question in one of the blog posts I've linked to below. The answer is - 'Duh!!Yes!'. Yes, these guys work directly with Bill Gates. If I remember correctly (I have to get this confirmed), Steven Sinofsky and Eric Rudder were both former technical assistants. And they went on to become senior vice presidents :)

Here are some initial articles and posts about the event.

Slashdot
News.com (CNET)
New York Times-

Indian papers

http://economictimes.indiatimes.com/articleshow/1325956.cms
http://www.deccan.com/Business/Business.asp#Microsoft%20in%20search%20of%20Indian%20talent
http://www.telegraphindia.com/1051210/asp/nation/story_5582805.asp
http://ciol.com/content/news/2005/105120912.asp

Some blogs referring to it
http://customerworld.typepad.com/swami_weblog/2005/12/microsofts_tale.html
http://spaces.msn.com/members/VolatileChar/Blog/cns!1pJFaU-KFFDMYqePiw9lsXaw!630.entry
http://abhijitworld.blogspot.com/2005/12/code-for-bill-bill-gates-new.html
http://theramesh.blogspot.com/2005/12/here-is-how-you-can-code-for-billgates.html

Blog searches

IceRocket, Technorati.

- Sriram Krishnan

37

sriram — Sun, 11 Dec 2005 12:54:00 GMT

As I stated in the morning the number 37 is key to getting results which contain the same digits

37 * 3 = 111

Then variations of this like 74 * 3, 37 * 6....... bring the results 111, 222,etc.

Then starts the next series 37037 and the other number people are trying to figure out.

(lot of you have figured that but I am not mentioning that here)

Again there are variations of that number BCDEF like *2, *4 producing different G values.

The next series is again interesting

12345679 * 9 produces 111111111 where this number 12345679 is again 37 * 333667.

Another cool thing is the variants of this 12345679 like *2, *4 versions

12345679 * 9 products 111111111 and misses 9 - 1 = 8 in the original number

24691358 * 9 produces 222222222 and misses 9 - 2 = 7 in the original number

The same again

98765432 * 9 produces 888888888 and misses 1.

All the best for tomorrow's problem.

- Perraju

Question for the day

sriram — Sun, 11 Dec 2005 12:32:00 GMT

A * BCDEF = GGGGGG

This is another question that's about working on the digits of a number.

It all starts with 37 * 3 = 111.After that you will see lot of numbers which produce the same digit in the resulting number and are in some way related to the original 37( like 74, .....)

Then comes this number BCDEF which brings in the next same-digit result number.If you observe closely,this is also related to 37 (may be not as straight forward as 37037 though).

Also,it changes the multiplier to 7. If you look closely, you'll see some hidden beauty.If you're interested, try and get the next number (whatever it is), which is not related to 37 in any way but has a result number with repeating digits.

Have a wonderful day

- Perraju

[ I posted the above for Peri (he had mailed it to me). Gosh - I feel dumb! - Sriram ]

Code4Bill begins!

sriram — Fri, 09 Dec 2005 13:08:00 GMT

Welcome to the Code4Bill blog! If you’ve found your way here, I’m sure you already know what Code4Bill is. If you don’t, here’s a quick refresher – Code4Bill is a contest aimed at finding the best student programmers in India. If you thought that you were the coolest coder around, here’s your chance to prove it. The prizes are huge – the top 20 get internships at Microsoft Research India and Microsoft India Development Center (where I work). The folks who successfully complete their internships will be given the proverbial red pill – a chance to become a Microsoft employee.

The winner gets a chance to work for the ‘man’ himself – Bill Gates - as a part of his technical assistant team.

Who are you?

Well, we’re the Code4Bill contest team. Over the next few posts, you’ll see quite a few of us blogging about..well..a lot of different things. I’m Sriram Krishnan – I got to write the first blog post as I’m the most good looking of the lot. [1] Seriously though, there are several cool people involved and several of them will be blogging here over the next few weeks.

When can I register?

As the official site says, registrations start on January 1^st. However, in the meantime, submit your email id and you can stay updated – we have several surprises in store for you. Of course, subscribe to this blog – we’ll be blogging updates as well.

What happens after that?

Sorry – that’s a secret. J Rest assured – it’ll be fun, wacky and test you in several ways. And we have several things planned in the interim – at the expense of repeating myself, stay tuned!

Anything else?

Since this is our first blog post, 48 65 6C 6C 6F 20 57 6F 72 6C 64!

- Sriram Krishnan

Notes:

1. Maybe slightly exaggerated