The Square Of Light

E4

So there’s this artist painting in his studio, when suddenly he reckons that what he wants is his canvas to get half the light it normally gets through a square-shaped open window. If this window is one metre by one metre and you’re not allowed to close the window, is there any way you could exactly half the light value coming into the room? Okay, one alternative is you could join the diagonal and board up either of the two right-angled triangle sections. But in that case the square shape of the window is not retained which for some reason the painter wants (you know how these artistic types are). Which means you can’t board up half the window to form two rectangles sections either.

In other words, though the two solutions are technically correct, the artist is not happy with them. That’s when you suddenly realise where the artist’s problem really lies. Because the simple fact is that you cannot normally double or half a square (and the window is a square). Meaning, one metre by one metre means an area of one square metre. Doubling this becomes two square metres. The sides of such a square would be the square root of two, which is an irrational number. Or, and this is the version we’re dealing with here, the square root of half a square metre is the square root of 0.5, which is again another irrational number — the decimals simply don’t know when to call it a day. That is, you could never get an exact value for the sides. So obviously you couldn’t construct a square of that proportion, area-wise, ever.

On the other hand, the painter is never stuck with any old number theory whatsoever (I told you what they’re like). He’s got a neat and practical solution to the theoretically impossible problem. Can you guess what it is?

DEAR MS:

Switched-Bulbs-Dept:

This question is easy! Turn the first switch ON and leave it on. Then turn the second switch ON, and then OFF after five minutes. Now we can find the switch that corresponds to the bulb. The bulb that’s glowing would be the bulb corresponding to the first switch. The bulb that’s warm would be the bulb correspon-ding to the second switch and the bulb without any change in temperature would be the bulb corresponding to the third switch.

• Athiyaman, athinalla@gmail.com

  The solution would be to switch on one light for some time, then switch it off. Then switch on the next switch and go up. Touch the lamps and see which is warm. Rest is simple.

• Guruprasad, hemaguru97@gmail.com

Great food for thought as usual. Flip on one switch and then switch on another one a couple of minutes later. Switch them off and go upstairs and check on the degree of warmth of each bulb. The warmest is the first switch and so on.

• Shantanu, mehtasingulf@gmail.com

Next trip to the basement I’ll carry a permanent marker.

• Lavanya Neliath, lavanyaneliath@gmail.com

I-Skate-Dept:

(The problem was: “You’re stranded in the middle of a frozen lake which is so slippery that you can’t walk or even crawl off. So how do you get off the ice?” — MS)

I would catch hold of a bag or shoe and throw it away from me. When I exert a force on it, it exerts an equal but opposite force on me due to Newton’s Third Law of Motion. Since the ice is slippery, we assume very little friction. That helps me to glide gleefully to the shore.

• Saifuddin Khomosi, saif_sfk@hotmail.com

‘Earing-Mosquitoes-Dept:

Mosquitoes emit their melodious buzz around all the exposed parts of our body. Only when they come near the ears, the emission becomes audible.

• Sheikh Sintha Mathar, sheikhsm7@gmail.com

ENDGAME(S)

1. Why does a pole-vaulter come charging at full speed whereas high jumpers approach the jump much slower?

2. Is it possible for a man to have once been married to his widow’s sister? (Before you think that’s impossible, let me tell you it’s not. — MS)

(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)