In a remote village in the Himalayas, which for some reason always seems like a juicily appropriate setting for a puzzle involving bells ringing at conveniently apt times and that fleeting sense of evanescent mystery, a Feast Day in capital letters to make it sound extra large and important is declared whenever the bells of the pagoda and the monastery ring at exactly the same time. So what else do we know? Well, the pagoda bell rings at regular intervals of a whole (as opposed to a half) number of minutes mainly because its less holier-than-thou manufacturer was more interested in maths than meeting his maker.

However, not to be outdone by this cheap stunt and basically to be different I guess, the monastery bell also rings at regular intervals, but of -- you guessed it -- a different whole number of minutes. And today in this best of all possible days in the world, by a stroke of an acausal connecting principle, the bells are due to ring together at 12 noon thanks to Carl Jung.

Nevertheless note kiya jaye that between those uppercased Feast Days, the bells of the pagoda and monastery ring alternately, and although they only coincide on Feast Days, they occur as little as a minute apart on some of the other days. If by now any of the above has made some sense of purpose then the last time the bells coincided was at 12 noon a prime number of days ago. Meaning, for what it’s worth, how many days ago was that?

THROUGHPUT

(The previous week’s reader problem was: “A vessel contains a liquid, 3 parts of which are water and 5 parts syrup. How much of the liquid must be drawn off and replaced with water so that the liquid may be half water and half syrup?”)

If X is the portion of the liquid to be withdrawn and replaced with water, then we have (1 - X) (3/8W + 5/8S) + X W is the quantity of liquid in which water (W) and the syrup (S) are equal. On rearranging the equation, (1 - X)*3/8 W + X*W is the quantum of water and (1 - X)*5/8S is the quantum of syrup both of which are equal to 1/2. On solving we get X = 1/5. Thus 1/5th of the liquid is to be withdrawn and replaced with water. -- P S Guruchandran, -- posaguarisi@gmail.com

If quantity to be replaced is x, the solution is that the revised quantity of water (3/8 - 3/8x + x) should be equal to revised quantity of syrup (5/8 - 5/8x). Thus the required quantity is 1/5th of original quantity. -- Tijender Gupta, tijender.gupta@gmail.com

(The second one was: “Why does the valve on a bicycle pump get so hot when you’re pumping up a tyre? It’s obviously not just friction because if you use a mechanic’s compressed air supply, the valve typically doesn’t get hot.”)

As the air in the pump tube is compressed, there is decrease in volume of air and an increase in collisions of air molecules. This releases energy in the form of heat which makes the valve hot. -- Ambar Roy, ambarroy97@gmail.com (Yes AR, but how about addressing the second part of the problem too? – MS)

In a mechanic’s air supply, the air is already compressed and is cooled. It gets cooled further as it expands and the valve doesn’t get hot. -- J Vaseekhar Manuel, orcontactme@gmail.com

(The third problem concerned how to beat a computer in a stick-picking-up game -- or not!)

The required correspondence is (1, 4), (2, 3), (3, 2) and (4, 1). Now whatever the user does, he will be left with one stick to pick last. The combination should be such that, whatever the user picks, the total number picked in each turn should remain the same. The computer just needs to make sure that it picks up the 20th stick every time. After four runs, the user is left with no option but to pick up the last one. -- Dr K N Murty, k_n_murty@yahoo.com

The computer must be programmed to pick up a number x such that x = 5 - y where y is the number picked up by the user. So it can be like 1-4, 2-3, 3-2, 4-1. By the 4th round 20 sticks are picked up and the user has no choice but lose! -- Jawahar, drjsurti@gmail.com

BUT GOOGLE THIS NOW

1. You see someone polishing a pair of leather shoes. Neither the polish nor the brush seem to have anything to do with the shine. Yet in the end the shoes shine. Why?

2. What connection does an elementary form of carbon have with a soccer ball?

— Sharma is a scriptwriter and former editor of Science Today magazine.

(mukul.mindsport@gmail.com)