All Above Water

What is the secret behind the erasing action of an eraser? That is, why can't a pencil eraser erase pen marks also?

E4
Want to know two cool facts about water that were never told to you in school, college, university, IIT, IIM or any other higher academe elsewhere in the universe - and won't be told even if you are reincarnated into the 23^rd century? (Incidentally these facts can also be used at parties to blow people's socks off permanently.)
Fact #1: Water is coloured. It's actually light blue. If you don't believe it, remember there's 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 think of not believing this again because that Google's still out there baying for your unbelieving blood.
But we'll go easy on you for 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?

DEAR MS

(The problem involved two magic squares and your job was to describe the exact relationship between them. - MS).
Square-Route Dept:
The relationship between the two is that the new square formed after adding the corresponding figures on the original squares is also a magic square. Likewise, the new square formed after subtracting the corresponding figures on the original squares is also a magic square.

• Ayan Joshi, ayanjoshi@yahoo.com

LCM of 45 and 21 is 315. So we multiply each number of the first magic square with 7 and the second one with 15. We get two different magic squares. Now sum of each of these magic squares, adding the numbers vertically, horizontally, or diagonally, is 315. This, truly, is magic!

• Dhurjati Sen, dhurjatidhurjati@gmail.com

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.

• Dr K N Murty, k_n_murty@yahoo.com

 (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?" - MS)
What-Goes-Up Dept:
If we assume 'x' to be the number of steps which are visible when the escalator is turned off, and 't' to be the time taken to walk down one step, then we can say that as I walked down the escalator in 50 steps, then x - 50 steps must have gone invisible to me in 50t units of time. Moreover, I take 125 steps to run up the escalator taking five steps for each one before. This means 125 - x steps must have gone invisible in 125/5 = 25t units of time. Thus, (x - 50)/50t = (125 - x)/25t; which gives x = 100 steps.

• Saifuddin S F Khomosi, saif_sfk@hotmail.com

 ENDGAME(S)

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, ktremail@gmail.com)

2. What is the secret behind the erasing action of an eraser? That is, why can't a pencil eraser erase pen marks also?

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

• Mindsport