When an archer shoots an arrow, the aim is made possible by all the other arrows taking all the other nearby paths, each with essentially the same action. Like, when you walk with a certain destination in mind, you’re not alone.

When walking, I know that my aim/ Is caused by the ghosts with my name./ And although I don’t see/ Where they walk next to me,/ I know they’re there ... (three words)Given a sufficiently long lever-arm, you can produce an arbitrarily large torque. This fact led a well-known ancient mathematician to claim that he could move the earth if given a long enough lever-arm.

One morning while eating my Wheaties,/ I felt the earth move beneath my feeties./ The cause for alarm/ Was a long lever-arm,/ At the end of which . . . (Two words)You have to now complete the two physics limericks using the number of words indicated.

THROUGHPUT

(The doddering Phoenix was: “There are two envelopes on the table and that they both have money in them, but one of them has double the amount the other has. You tell me to pick one, and I open it to find Rs 20 in it. You then give me an opportunity to trade envelopes. Should I?”)

Yes, he should opt for the exchange. Suppose in the envelope picked up, the money is X. There is a 50% chance that the other envelope contains money of X/2 and a 50% chance that it contains 2X. So the expected value in the second envelope is 0.5*X/2 + 0.5*2X, or 1.25X. So he is likely to end up earning more money. -- Prof. S Manikutty, manikuti@iima.ac.in

The other envelope is either the bigger of the two, in which case it has Rs 40 in it, or the smaller of the two, in which case it has Rs 10 in it. So by switching I have a 50% chance of losing Rs 10 and a 50% chance of winning Rs 20. I think it is worth taking the risk of trading the envelopes! Shashi Shekher Thakur, shashishekher@yahoo.com

Yes, I would choose to trade the envelopes but will be unreal and keep the money. You’re asking to trade the envelopes not money! -- Hema Raghuveer, har2007inuk@yahoo.co.uk

Is this not similar to the Monty Hall problem? -- A V Ramana Rao, raoavr@gmail.com

(The second problem was: “Given that there is only one way to draw a five-pointed star, and no way to draw a six-pointed (in continuous lines, that is) and two ways to draw a seven-pointed one, how many different ways are there to draw a 1000-pointed star?”)

We need to figure out the numbers between 1 and 500 which are co-primes with 1000. Now, there are 250 even and 250 odd numbers between 1 and 500. Of the 250 odd numbers, one in five end with digit 5, leaving 200 numbers which end in 1, 3, 7 and 9. All these numbers are co-primes with 1000. So, there are 200 different ways to draw a 1000 pointed star. Actually 199, because joining every point will give a polygon and not a star. -- Saifuddin S F Khomosi, Dubai

(The third one was: “Two words are synonyms. Just by the addition of a suffix to each word, they become antonyms (same suffix for both words). What are they?”) Jail = Prison (synonyms); Add suffix “er”. Jailer and Prisoner are antonyms. -- Dhruv Narayan, dhruv510@gmail.com

PRICE, WORTH and VALUE have all more or less the same meaning. Add the suffix LESS to each of them: PRICELESS means ‘precious’ but WORTHLESS and VALUELESS mean exactly the opposite. -- Rajagopalan K T, ktremail@gmail.com

“Hard” and “strenuous” are synonyms of “laborious”. But when “ly” is added they become antonyms; “hardly” and “strenuously”. A man working “hardly” doesn’t work at all whereas a man working “strenuously” does hard work. Balagopalan Nair K, balagopalannair@gmail.com

BUT GOOGLE THIS NOW

1. Solve numerically: TWO + THREE + SEVEN = TWELVE, given that each alphabet stands for a distinct digit 0 thru 9 (both inclusive). (Submitted by Sheikh Sintha Mathar, sheikhsm7@gmail.com)

2. Here’s an easy one but one that should take a while to solve. It’s also way up and over all uber interesting facts and one day you’re going to thank me for making most doctors at parties look like fools. What’s common to David Pritchard, Horace Wells, Elsie Widdowson, Maurizio Montalbini, Jack Barnes, Donald Unger, Barry Marshall, Henry Head, Stubbins Ffirth and Jesse Lazear? Here’s a hint: one of them won the Nobel Prize and one the Ig Nobel Prize.

**Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)**