Wednesday, February 4, 2009

Marching cadets and trotting dog problem

Hi Zubin:

Here is a problem I ran into in "Martin Gardner's New Mathematical Diversions from Scientific American". It is simple enough that you can describe it while talking with friends at a break point or during a drive...

The problem:

A group of cadets is marching in a 50m x 50m square formation. Their pet dog starts from the middle of the back (A in figure below), runs to B at the front, turns back instantaneously, and runs to A in the rear again. In the meantime, the formation has moved forward by 50m. Assuming the dog runs at constant speed, how far did it travel?


My first guess was that the dog runs 50m + 50m forward, and then 50m back, so 150m. But of course this is an overstimate, since actually, it's turning back from some point well before 100m ahead.

(Read on only if you have tried it now...)






If the dog's speed is v m/s and the formations is u m/s, then while running forward, the dog's speed is v-u with respect to the formation, so it runs forward for 50/v-u seconds. Then it runs back for 50/v+u seconds. In the meanwhile, the formation has taken 50/u seconds to march 50m.

SO - the sum of these two times is 50/u. You can now eliminate 50 and and u and solve for v/u, which will give you the answer since 50/u . v is the distance he runs.

So - what do you think - will it come down to a quadratic equation?

Let me know what you get!


Friday, October 24, 2008

chess, SAT, and diwali

Dear Zubin:

these days i have introduced the chess clock in the tea room we have at office - i have been playing occasional games with others, none of whom, like me, have ever played with a chess clock. everytime i play, i remember how you had learned chess for the first time, and then how you first started playing in the library, and then in the RTM, and now you are gradually going up. in between, it was i who learned from you, for example, the protocols of using a chess clock...

thank you!

i wonder about so many things, zubie. your SAT scores. you had a test in the library on august 16 - wonder how that went - most likely you were around 700 in quant at least, and verbal was also going there. now the main SAT is coming up in a month or so you still need to do more on verbal - one way is to have everyone in the family use the words that are there in the wordlist - that way not only you but everyone can expand their vocab; but for you, there is no better way to go ahead on vocab than to use these words in everyday conditions.

other than that, there is this obama fever in the air. it seems a good thing for the USA after a long time. i think now is a good time to invest in the stock market, now that it is so low. what do you think?

what else? i am of course quite happy about Anand's 3-game lead... are you guys managing to follow these games, I wonder.

out here diwali is around the corner. this is the time when every house is lit with candles, and children burst firecrackers. i have almost never been with you at diwali - but of course we have burst some crackers together on fourth of july, thanks to the hurleys.

so many things going on. trust you are doing well. so much, so much, i want to wish you well. all of you, in everything you do.

good morning!


world chess championship -- chess club at school? or at the lib?

Dear Zubin:

I am sure you are quite excited by the WCC08 going on, the first match of which was drawn yesterday.

It may be a good idea to form a local group - perhaps at school - but may be it would be better in the library - where some stronger people may also be there - to consider the matches soon after they happen. Typical matches would be starting at 9 AM your time, and normally may be finished by about 2 PM end of school day...

So on the days of the match you can then have a small conclave going over the games!! If it is the library you could even bicycle down - today's high for e.g. was 65 degrees - so maybe it is do-able... trust the bicycles are in running condition...

Here are the dates of the WCC:

Game 1: Tuesday, October 14
Game 2: Wednesday, October 15
--> gap this Thursday
Game 3: Friday, October 17
Game 4: Saturday, October 18
--> gap Sunday
Game 5: Monday, October 20
Game 6: Tuesday, October 21

Game 7: Thursday, October 23
Game 8: Friday, October 24

Game 9: Sunday, October 26
Game 10: Monday, October 27

Game 11: Wednesday, October 29

Game 12: Friday, October 31

Tiebreak: Sunday, November 2

All rounds, including the tiebreak, start at 3 p.m. local time (= 9 a.m. ET).

Also, I am not sure you are playing in the Brother John tournaments - probably they are not as good. Anyhow I am forwarding something for the coming weekend.

I heard you did well in a tournament and also got some money. Good for you. It would be nice if you mailed me occasionally. As you may know, I tried calling some 10-15 times on Oct 3 for dada's birthday but no one picked up, which is why I thought I would start writing.

Well - hope you are enjoying your chess!!



Saturday, October 11, 2008

shubha bijaya শুভ বিজয়া!

dear Zubin and Zagreb:

here's wishing you a
শুভ বিজয়া

in case you can't read that (heh heh!) the alphabets are
  • "sh+u"শ+ু = শু
  • "bha" ভ
  • "b+i=bi" ব+ি = বি (if ি and the ব are reversed, here's a fix)
  • "ja" = জ
  • "y+A=yA" য়া
shubha means "good, propitious", and bijayA means victory or celebration. you will find the text in this image as well:

every year around this time, i am sure you hear the "shubha bijayA" greeting quite often. bijayA is the tenth day of durga puja, when bengali's celebrate the the victory of durga over the demon mahishasur. the image above shows a modern sculpture of durga, where the devi is shown killing the asura who is pinned down by her lion.

bijayA is also a time when we visit relatives, and praNAm our elders. males do kolAkuli, hugging each other thrice, as you know. typically this festive greeting season extends from the end of durgA pujA on the tenth day of the waxing moon (this past oct 9) till the next new moon day or amAvasyA (that is the diwAli or kAli Puja day, which will be oct 28). you can wish anyone you meet in this period with "shubha bijoyA".

and the good thing is that usually, those whom you greet will offer you sweets and snacks !!

lots and lots of "AshirvAd" for you both of you on this bijayA!! may you eat a lots of goodies in this time! may you do the best in everything you do!



Friday, October 10, 2008

the sad story of douglas prasher

Dear Zubin:

Today I came across a news item which I thought I would share with you.

This is about the Nobel Prize for chemistry. The prize was given to three chemists, who had worked out how the jellyfish manages to glow in the dark. The jellyfish does this by generating the Green Fluorescent Protein (GFP), which glows. The jellyfish grows this protein under instructions from a particular gene, and the importance of this discovery is that this gene can be added to other dna cells, and can be used to trace when these cells become active. It is a very important tool in biochemistry today, in all sorts of investigations.

But the point is that this nobel prize would not have been possible if these chemists did not have access to this gene.

It turns out that the gene was isolated by a researcher called Douglas Prasher (see this illustrated history). Prasher was also the first to note that GFP could be used in this way as a fluorescent tracer on genes. This is the process that was finally completed by the scientists who got the Nobel (see this report at forbes magazine).

When the scientists separately requested Prasher for the gene he gave it to them freely. Roger Tsien of UCSD said in an interview:
"So I found his phone number, called him up, and to my amazement he was willing to give out the gene."

After Prasher was mentioned by Tsien in several interviews, some journalists started wondering where he was today. Clearly, Prasher is a biologist of some importance. However, it turned out he did not get tenure at Wood's Hole and joined industry. He was eventually laid off from Pfizer some years back, and some journalists from NPR traced him down - it turns out that he has been driving a limousine service in Huntsville Alabama for the last two years.

NPR reporter Dan Charles says:
Prasher doesn't have any regrets about giving away the gene. Tsien and Chalfie did great work, he says, which he probably couldn't have done because the National Institutes of Health had rejected his funding proposals.

The story broke on October 9, and got a lot of coverage the next day - an excellent wikipedia page on him came up almost immediately. Possibly you and dada and mummum are already discussing this, but I thought I would share it with you anyway.

Quite a sad story, wouldn't you say, for such a man?