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A divisibility puzzle

Found an interesting puzzle while exploring Hari’s blog As the puzzle is very small, republishing it here. Here it goes..

Find a number x when divided by n leaves a reminder n-1,
where n ranges from 1 to 10.

I just tried to do something with the basic rules of divisibility for a few minutes before the programmer in me woke up and said “Do you really want to solve the problem? You can get the solution in no time”. Python was ready to swallow the mathematician in me

ab = range(1, 15000)
for i in range(10, 1, -1):
  ab=[x for x in ab if((x%i)==(i-1))]
print ab

Solution set: [ 2519, 5039, 7559, 10079, 12599, ... ]

The interesting fact is that the difference between any two elements in the solution set is a multiple of 2520 which is the smallest natural number divisible by all numbers from 2 to 10. Subtracting 1 from 2520 makes it indivisible by every number from 2 to 10. Wow! Having found out the solution, now I back track to solve the problem. Any mathematicians out there? Please help me solve it using the rules of divisibility

happy new decade

I see some excitement in me this year even though I don’t like the idea that a new year is a new beginning. After all, every new day is a new fraction of its year. The same time last year, I was just leading a less meaningful life. My return to Chennai in Jan 2009 triggered the positive change I was looking for I’m unable to believe that almost one full year has passed away after that!  With the end of the most outstanding year in my life, there goes silently, the decade that completely changed my life in a way I never imagined. Just because it was good, I cannot retain it anyway Let’s move on.. Well, forgot to wish you!  I wish you a happy new decade! Unlike the usual wishes, that doesn’t literally mean “I’m not going to bother about you in the next decade”

Deepavali special!

There’s one more week for the festival. But I’m in a festive mood already   Personal life is eventful these days, especially at week ends.  After many weeks of teaching as part of Kanini classes, we(teaching volunteers) conducted an assessment test on MS Word at WET center, last week. The results are amazing with the average around 29 out of 50 marks. The kids have done a great job! Don’t ask what is so amazing about it. It took me first two semesters of my college life to understand what is a computer and what can be basically done using it. And it took even more time for me to get comfortable with very basic applications. I still remember how my fellow mates Srini and Vijay used to teach and help me out.  But these kids have learned about them in a couple of months and that too from teachers like me Meanwhile, Kanini classes are going great at VMT center also. I’m really getting excited like a child every week thinking about  planning classes and incorporating new ideas that come to my mind once in a while. At job, I’ve started working on designing a web service for HeyMath! to serve content. Right now, it has not really reached a good shape. I’ve this question related to the task. Pointers are welcome

Time to mix some bad news in between. I’ve lost my mobile for the third time in my life. First time I lost it, next time it was stolen at some public place, third time it got stolen at my office. I never like repeating mistakes more than once but this has raised “Yaanaikum adi sarukum” exception I was angry on myself  for my carelessness but nothing more can be done about the past. I’ve wasted around 17K rupees on mobile phones so far It has been almost 3 weeks since it happened. So, Yes! I’m living and I can live without a mobile!!

To those, wondering about the relation between the title and the content, Happy Deepavali(Diwali) wishes in advance!! Don’t you know how tough it is to come up with a title, especially when we are not writing about anything in specific?

Life Logger #2

I’m writing this down at the end of a happy week in my professional as well as personal life.  The main source of joy was the satisfaction I had, after completing two features for HeyMath! – Previous Years’ Assignments and Check Your Understanding.  This was my first hands-on experience with a web application but the features were not really complex. May be, they canceled out each other and ended up giving good results Anyway, I completely enjoyed developing them right from design phase to user interface coding. Lot of interesting things learnt along the way!  Moving on to the other side of my life, I’ve started making use of week ends in a responsible way through Bhumi’s Kanini program trying to make some underprivileged kids computer-literate.  It gives me immense satisfaction. Also I’m really thinking forward about how can  I help those kids through Bhumi’s Career Counseling program.  And my birthday (Aug 5)  this year needs a special mention. I never think of  it as any special day, but this time it had quite a few special moments! One of my best friends left to US for higher studies that night. Three hours before that he was at my home wishing me and sharing a lighter moment. It was very very special, as I met him after a long time!