The Hole Truth

Now, in a vague topological sort of way, the navel basically is a hole in the middle of a baby.

E4
I think I may have made a pretty profound medical discovery recently. See, I was in a friend's room the other day where she has a poster that says: "If you concentrate on your navel for a long time, sooner or later you're sure to discover some lint". So I did (not find lint, but concentrate) and found that it was like the old problem about heating a circular disc of metal with a hole in the middle. Like, does the hole get larger or smaller? Well larger obviously, and proportionately too, because the whole thing expands.
Now, in a vague topological sort of way, the navel basically is a hole in the middle of a baby. Meaning as the baby grows, so should the navel, right? So by the time a child finally stops growing in his or her middle teens or whenever, the navel - growing along proportionately - should actually have become enormous; At least about 6-8" or so in diameter, across the belly. Yet, nothing of the kind happens. Is there some unknown negative biological force like dark energy at work here for which I should be credited and given a prize?

DEAR MS

For-Whom-It-Tolls Dept:
(Regarding the pagoda bells problem) Number of minutes in a day = 24*60 = 1,440. The bells ring alternately, implying that we are dealing with x & (x + 1) minutes of time intervals. Further, x*(x + 1) = 1,440*N, where N is prime, as per the given information. The easiest way this could happen is if 1,440 is one of the two intervals, the other being either 1,439 or 1,441. Of these two 1,439 is a prime number. In other words, N = 1,439 or the time intervals are 1,439 minutes and 1,440 minutes and thus the two bells chimed together at 12 noon, 1,439 days ago.

• Ajit Athle, ajitathle@gmail.com

(The other leftover problem was: "You see someone polishing a pair of leather shoes. Neither the polish nor the brush seem to have anything to do with the shine. Yet in the end the shoes shine. Why?" - MS)
Spit-And-Polish Dept:
When the shoe polish is applied to the shoe with a brush, it causes friction that liquefies the polish. This allows the polish to fill any cracks on the shoe surface. The shoe polish then dries to a dull finish. The final process of buffing the polish with a buffing brush or cloth causes the polish to again liquefy and even out on the shoe surface, making it shiny and reflective. The result is a protective layer that is very glossy.

• Saifuddin Khomosi, saif_sfk@hotmail.com

Papering-Over Dept:
(Regarding the rectangular sheet of paper problem) The ratio is 3:1. A will fall on EF at Q and G will fall on AX at, say N, if the paper is folded along a line cutting across AD and AB at, say Y and Z, respectively, supposing that we're cutting AQ at J, EF at K, AX at L and GH at M. Obviously AY = YQ, AJ = JQ, AK = KQ, AL = LQ and GM = MN, etc. Hence the ratio of the angles XAD and QAD is 3:1.

• Abhay Prakash, abhayprakash@hotmail.com

(The last problem was: "The words POISED, OTPITA, IPITOR, SITTER, ETOELE and DARREM written one below the other form a square whose columns read the same as the rows.  The problem is to rearrange the letters in the grid so that all the six words are valid." - MS)
Square-Peg Dept:
I managed it in half an hour after figuring out which diagonal was the correct one. Here's the rearranged square with the first word on top and last one at the bottom: PASTOR, ATTIRE, STUPID, TIPTOE, ORIOLE, REDEEM.

• Alan D'Souza, iamaland@gmail.com

ENDGAME(S)

1. Fighter planes use flares to avoid missiles fired at them. Wouldn't a flare in fact give away a reading to their approximate location?
2. Why are the rear wheels of some three-wheeler vehicles inclined inwards? Wouldn't an outward inclination give it more stability? 

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

• Mindsport