Want to know two cool facts about water which were never told to you in school, college, university, IIT, IIM or any other I’s of higher academe elsewhere in the universe -- and won’t be told even if you reincarnate in the 23rd century? (Incidentally these facts can also be used at parties to blow the socks off people’s heads permanently.)
Fact #1: Water is coloured. It’s actually light blue. If you don’t believe it remember there’s a whole bunch of Google out there for you to quietly consult and keep shut forever afterwards. Fact #2: If you want to cut a sheet of glass like a window pane for instance, with a pair of scissors (yes, scissors), simply do it under water in a basin full of it. Don’t even THIINK of not believing this again because that Google’s still out there baying for your unbelieving blood.
But guess what -- we’ll go easy on you now. ABCD is a rectangular sheet of paper (A at top left, rest clockwise). EF and GH are lines perpendicular to AB such that AE = EG = (AB)/4. AX is an arbitrary line through A meeting BC at X. The paper is folded such that point G falls on AX and corner A falls on line EF at point Q. What is the ratio of the angles XAD and QAD?
(The problem involved two magic squares and your job was to describe the exact relationship between them.).
If the corresponding numbers in the two grids are added, we get 9, 31, 26 in the first row, 39, 22, 5 in the second row and 18, 13, 35 in the third row in which case each row, column and diagonal adds up to 66. If the corresponding numbers of the second grid are subtracted from the corresponding numbers of the first, we get 1, 13, 10 in the first row, 17, 8, -1 in the second row, 6, 3, 15 in the third row in which case each row, column and diagonal adds up to 24. -- K Sundaram, email@example.com
This is an “Alphamagic square” for which the number of letters in the word for each number generates another magic square. Thus the second square is formed with the number of letters in “five”, “twenty- two”, “eighteen” for the first row; “twenty-eight”, ”fifteen, “two” for the second row and “twelve”, “eight”, “twenty-five” for the third row. Thus the second square is formed with numbers 4, 9 and 8 in the first row, 11, 7 and 3 in the second and 6, 5 and 10 in the third, which also happens to be a magic square. -- Dr K N Murty, firstname.lastname@example.org
(The other problem was: “Walking slowly down a descending escalator you reach the bottom after taking 50 steps. Then running up the escalator at five times the walking down speed you take 125 steps. How many steps will be visible if the escalator is turned off?”)
Let v be the speed of the escalator in steps per second. Let N be the number of steps that you need to take when the escalator stands still. Downwards (along with the escalator), you walk, let’s say, 1 step per second. You need 50 steps, so that takes 50 seconds. This gives: N - 50*v = 50. Running up you take 5 steps per second. You need 125 steps, so that takes 25 seconds. So now we’ve another equation: N + 25*v = 125. Solving these two we get: N = 100 so that when the escalator stands still, 100 steps are visible. -- Ajit Athle, email@example.com
Let’s say I am moving at a speed of x steps/sec while moving down. So, I will be moving up at a speed of 5*x steps/sec. Further, let’s say the escalator is moving at y steps/sec and it has N steps visible when it is not moving. It takes t1 seconds for me go down and t2 seconds to go up. So: t1*x = 50; t2*x = 125. Now, in t1 seconds escalator and I together take N steps. Ie, t1*x + t1*y = N. Similarly, 5*t2*x - t2*y = N. Solving, we get the value of N as 100 steps. -- Dhruv Narayan, firstname.lastname@example.org
BUT GOOGLE THIS NOW
1. The words POISED, OTPITA, IPITOR, SITTER, ETOELE and DARREM written one below the other form a square whose columns (top to bottom) read the same as the rows (left to right) in order. The only snag is that except for POISED and SITTER, the other words make no sense. The problem is to rearrange the letters in the grid so that all the six words are valid and the row-column correspondence remains. – (Submitted by Rajagopalan K T, email@example.com)
2. What is the funda behind the erasing action of an eraser? That is, why can’t a pencil eraser erase pen marks also?