If you’re familiar with plastic indoor Christmas trees you’re familiar with all those shiny little polished metallic like balls you have to hang on them, right? I guess by now you also know the secret behind how those balls can give you a clear picture of nearly the whole room in reflection too. Something like a super fisheye lens in reverse. But how do you think it’ll reflect a point source of light in an otherwise darkened room?
Of course you can cheat but you’ll look so stupid all alone out there in the dead of gloom in your pyjamas or nitie, trying to prove a point source of light.
THROUGHPUT
(The chess problem was: “The rules of chess are changed as follows. White and Black alternately make two legal moves starting with White. Assume Black has a winning strategy which White knows about. Can we say the that even if White does not win he or she can always guarantee a draw?”)
Considering I got no (spelt GNOW with G and W silent) answers at all I’ll give a hint instead. White doesn’t have to remain white. With his first two given legal moves he can instantly turn into Black! – mukul.mindsport@gmail.com
(The other problem was: “Consider a cube. When it’s painted red and cut into one-inch cubes, there are (a) twice as many cubes with one red side as there are cubes with two red sides; and (b) there are eight times as many cubes with no paint as there are cubes with three painted sides. What are the dimensions of this cube?”)
The cube is of the size 6” x 6” x 6”. The clue is, there are always 8 cubes with three painted sides irrespective of the size of the original bigger cube. This leads to the number of cubes with no painted sides to 64, which by themselves form a cube of 4” x 4” x 4”. Now add 1” cubes on all sides and you get a cube of 6” dimension, consisting of 216 smaller 1” cubes. The number of cubes painted on one side is 96; painted on two sides is 48; painted on three sides is 8; the number without paint any side is 64. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
Answer is a 6-inch cube. Any cube will have 8 corner side cubes painted on 3 sides. Hence unpainted are 8*8 = 64 cubes. Together they are 72 cubes. The balance one side painted and 2 side painted are in 1 : 2 proportion. Together say 3x. Now sum of number of cubes is 72 + 3x. This must be a perfect cube. By trial 216 is a perfect cube and 216 -72 = 144 is divisible by 3. Giving 48 + 96. Taking 6 cube root of 216 gives the answer satisfying all data. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com
(Among the first five who also got it right are: Balagopalan Nair K, balagopalannair@gmail.com; Prof S Manikutty, manikuti@iima.ac.in; Narayana Murty Karri, Dhruv Narayan, dhruv510@gmail.com; K T Rajagopalan, ktremail@gmail.com; Abhay Prakash, abhayprakash@hotmail.com)
(The third problem was: “Take oil and water in a beaker. The oil floats in a separate layer on top. In which direction should one accelerate the beaker to mix the oil and water?”)
The beaker should be rotated about its central axis to have exert the creation of centripetal force on the differently massed water and oil for mixing of oil with water. -- Nrusingha Behera, ncb123.age@gmail.com (Nope -- MS)
When a car accelerates or brakes, an object tends to move backward or forward due to the inertial forces. If you are in a car and it brakes suddenly, the car slows down but you don’t and hence are thrown forward. This is inertia. But inertia is a property that depends on the mass of the body. More the mass more is the inertia. Oil is lighter than water and so has less inertia. Thus when we accelerate the beaker (downwards), the lighter oil moves forward (ie, also downwards) thus aiding it to mix with the water. -- Shashi ShekherThakur, shashishekher@yahoo.com
BUT GOOGLE THIS NOW
1. Discovering his scales are faulty, a grocer weighs customers’ orders in two halves, putting the first half in the left-hand pan and weights in the right, then vice versa. Is this fair to both his customers and himself?
2. A cat and dog run a race, 100 metres straight and return. The dog leaps three metres at each bound and the cat only two metres, but then she makes three leaps to his two. Under these circumstances, what is the second answer to the question: Who wins the race?
Mukul Sharma
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)