M i n d s p O r T What’s with the wad?
E4 Want a clue on how to solve the problem downstairs of this para? Take a look at the two people who’ve given solutions to the crumpled wad of paper problem coming up below that. You’ll find that if you think laterally, there’s a tactical similarity operating between each and hopefully you’ll be able to squeeze your respective craniums betwixt them.
A monk rises at sunrise and climbs a tall hill to meditate ( as if he couldn’t have meditated in his kitchen). The path is a narrow spiralling one to the summit and he walks at varying speeds, even stopping frequently to rest. After meditating for some days, the monk comes down — starting again at sunrise — with varying speed along the same path. Can it be proven ( and please, without going into quantum chromodynamics, Hamiltonian graphs or Hilbert spaces) that there is a spot along the path that the monk will occupy on both trips at precisely the same time of day? part is irrelevant. Remove from the wad the paper corresponding to the irrelevant area. Now the area covered becomes smaller, giving rise to a fresh irrelevant portion. Repeat these removals. It will end with the wad being reduced to a point above its corresponding point.
— Altaf Ahmed, ctrlaltaf@ yahoo. in
Simply put, if you take a map of a country and lay it out on a table inside that country, there will always be a point on the map which will be on top of the same point of the country. A sort of ‘ You Are Here’ indicator! — Saifuddin S F Khomosi,
saif_ sfk@ hotmail. com
( Second problem: “A cube is made of white material but its exterior is painted black. If the cube is cut into 64 smaller cubes of exactly the same size, how many of the cubes will have at least two of their sides painted black?” — MS)
High- i- Cube- DEPT: The number of small cubes unpainted, one side painted and two sides painted, have standard relationships with the original cube’s size. Three sides painted will always be 8 pieces, irrespective of the cube’s size. For a cube of side n units ( n = 2 or more), the number of cubes painted on two sides will be 12*( n - 2), which, in this case is 24. Hence the total number of small cubes with at least two sides painted will be 8 + 24 = 32. — Sheikh Sintha Mathar,
sheikhsm7@ gmail. com ( Among the first five who also got it right are: Niraj Nandish, nirajnandish@ icloud. com; Jaelyne Tauro, jaelynetauro@ gmail. c om; Si ddharth Patkar, s i ddhpatkar@ gmail. com; Ayan Joshi, ayanjoshi@ yahoo. c o m; Pri y anka Awatramani, pr i y a nk
ag1010@ gmail. com.)
( The third problem was: Can a ball roll on ice in — ideally — zero friction conditions? — MS)
A ball on a frictionless surface, when rolled, keeps on rolling or rotating at the same place, as there is no friction to push it forward or act on it. — Ramakrishna Bhogadi, rambhogadi@ gmail. com
ENDGAME( S) 1. Take some detergent powder in your palm and place it inside a bucket of cool water. As the powder rises, the hand feels hot. Does it make a difference if done in warm water? 2. You’re given a large bucket filled with water, a wooden ruler and a soccer ball. Determine ( approx.) the diameter of the ball using only these items. ( Mukul can be reached at mukul. mindsport
@ gmail. com)
TAURUS apr 20 may 20
You may see yourself as less appealing than usual, causing you to cling to whatever makes you feel secure. You may find yourself preferring your own company at times. A relationship seems more serious now, and having fun is secondary to dealing with an issue of importance. You will be more open in what you reveal to those you like.
GEMINI may 21 JUN 21
A serious tone seems to underlie this week and you will do best to focus on substantive issues rather than unnecessary concerns. Working hard and being patient is preferable to forcing a matter and, if you experience delays and frustration, don’t worry as they will soon pass. Watch your diet and general health.
CANCER JUN 22 JUL 22
Concentrating on specifics, rather than on generalities, may delay you; however, it will keep you on track. Communication with others may need compromising, as you will be reluctant to give ground on an issue wherein your position is set. Without being rigid, you can take on any experience or activity with confidence.