he architect of the 'impregnable demon fortress' was Mayasura, and as usual, the troublesome boon was granted to the Asuras by Brahma. The ancient texts call it Tripura ("the three cities"), which consisted of three mobile structures: 1) an iron city on earth 2) a silver city in the sky, and 3) a city in heaven made of pure gold. It is uncertain whether they were coaxial discs, or concentric spheres, but the whole construction resembled a giant cosmological lock and clock.

The mythological cities kept moving in such a way that they were never aligned, except once in many millions of years, like planets during an eclipse. At this syzygy, it is said - the moon would be in conjunction with the nakshatra Pushya, somewhere in the constellation Cancer. Only one person had the power to shoot an arrow such that it would pierce through all the three cities simultaneously at this moment, destroying them forever. Not just the archer Arjuna or a roadside Robin Hood – the seemingly impossible task was accomplished by Lord Shiva himself. The name of his arrow was Pinaka, the form taken by Lord Vishnu.

By a strange coincidence, the name of a friendly waiter at the Java City cafe in Kormangala is Jagadish. Today I saw him playing a computer game while I paid the bill – a Robin Hoodesque figure on the left of the screen shoots horizontal arrows, straight at a circle drifting vertically, up and down on the right. It is a very trivial game to program; I made something identical in eighth grade in Jaipur, but playing it is even simpler. You wait for the circle to come towards middle height, the target point -  and shoot just before it aligns with the arrow. Depending on the timing, distance and speed, you score bull's eye or less.

Now imagine if you had two circles instead, drifting in the same vertical path, and the aim is to shoot through them every time they come together. Let us say the first circle passes the target point once every 2 minutes, and the second circle every 3 minutes. You will get one opportunity every 6 minutes, because 6 is the "lowest common multiple" (LCM) of 2 and 3. Similarly, circles moving at periods of (say) 8 and 34 seconds would provide an opportunity every 136 seconds. However, that exact moment would only be the keyhole if the circles were moving in the same line. If the paths are slightly far apart, the horizontal distance the arrow takes to travel from one circle to the next will have to be considered. The 'lowest common multiple' (LCM) will not help us now. We are assuming that all things in this puzzle travel at some constant speed. Now we add one more circle, so we have three moving targets, at a little distance from each other, and to be pierced by a single arrow.

eanwhile...inside the shape-shifting fortress of Tripura...as eons pass in prosperity, the Asuras forget their primordial weakness and start sinking into their devilish ways while acquiring more and more power over the heavens. Brahma directs the despondent devas to approach Shiva and seek his help, and Shiva orders them to design his chariot for the attack. "Brahma held the reins, Vishnu was the arrow, Agni was its tip, and Vayu inside its feathers..." goes the legend.

Let us say that the cataclysmic arrow was to be shot by Shiva, from a distance of 7 years from the Iron City's side, which arrives at the target line every 837 years. 1 year further down the line is the Silver City, which arrives at the target line every 982 years, and the last target for the arrow is 15 years further – the city of Gold, which passes the target line every 137 years. One single line, one arrow, three moving cities.

Here's the question: assuming that Shiva succeeded at the first opportunity...what was the age of Tripura when it was destroyed?

Hint: Use the "Chinese Remainder Theorem".

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Answer: We have three congruence equations: X = -7 (mod 837), X = -8 (mod 982), and X = -23 (mod 137). By the Chinese Remainder Theorem, the first such occurrence would be at X = 70,811,030 years. (I've calculated this on a computer algebra system, not by hand! Please report any errata to This e-mail address is being protected from spambots. You need JavaScript enabled to view it )