The Write Stuff

E4
What's the difference between a vegetable and a fruit? As a rule of thumb, if it's sweetish, it's probably a fruit and if it's not, then probably a veggie. This works okay till you learn that there's another definition which happens to be a botanical one and it's much more definitive. If the thingy has a seed or several of them inside then it's a fruit; if it doesn't, then veg. With that total trivia in hand, have a nice five minutes figuring out what's what you eat. Only remember that bananas have seeds and so do tomatoes and cucumbers.
And if your time's up, then know that I've written my name in 1 cm letters with a pen without any other help than my naked hands. I can make the letters grow (but not the material on which they're written) to 2 or even 3 cms and then make them decrease to their original size. Also, I can destroy the letters (without affecting the material where they are written) and then rejoin them without using any adhesive substance. If I've not written my name on sand, skin, a rubber balloon or any other ridiculous place, then where did I write it?
 
DEAR MS
(The problem was: "A hydrogen balloon is rising skywards. Its potential energy is increasing and so is its kinetic energy. Something wrong here somewhere?" - MS)
 
Energy-Deficit-Dept:
Yes, something is wrong with this balloon. Hydrogen is lighter than air, so it keeps on rising. The potential energy of a body depends on its height, so it increases. Because the air at higher altitudes is lighter, the hydrogen balloon should gradually slow down while rising up. So the kinetic energy should decrease, not increase.
- Siddharth Patkar, siddhpatkar@gmail.com
The PE of the balloon does increase as it rises. But this is because the air above moves down to displace it, losing PE in the process. A given volume of air loses more PE sinking than the balloon gaining it (over a certain distance). Thus the potential energy of the entire system decreases as the balloon rises. We should keep in mind that the balloon rises due to the buoyancy of air and not due to work done against gravity.
- Saifuddin S F Khomosi, saif_sfk@hotmail.com
 
(The Lewis Carroll problem was: "The Governor of Kgovjni wants to give a very small dinner party and invites his father's brother-in-law, his brother's father-in-law, his father-in-law's brother and his brother-in-law's father. Can you find the number of guests?" - MS)

Father-Out-Law-Dept:
The Governor's father's brother-in-law, his brother's father-in-law, his father-in-law's brother and his brother-in-law's father . . . they're all the same person!
- Surya Narayanan Krishna Moorthy, surya661666@yahoo.com
 
If the members of the Governor's family marry within the family, the answer is 1. This is because his father's brother-in-law, his brother's father-in-law, his father-in-law's brother, and his brother-in-law's father are all one and the same person.
- Jaelyne Tauro, jaelynetauro@gmail.com
 
You could call it brother-in-law or even father-in-law, but ultimately the guest list works out to ONE!
- Gadepalli Subramanyam, gsmani174@gmail.com
 
(The third one was: "When Mike was twice as old as Judy was when Mike was three times as old as Judy was when Mike was as old as Judy is now, Judy was half as old as Mike was when Judy was half as old as Mike is now. So exactly how old are they now?" - MS)
 
Mike's age works out to 14J - 8M while Judy's age turns out to be (3/4)M - (J/2). The difference in ages must be the same. We get 39M = 62J as the equation. The only whole number combination is 62 and 39.
- Saishankar Swaminathan, saishankar482@gmail.com
 
ENDGAME(S)
1. Can a ball roll on ice in (ideally) zero friction conditions?
2. 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?

(Mukul can be reached at mukul.mindsport@gmail.com)