The Last (Juggling) Act

E4
First, the bad news. For reasons which will not be given (not because they're secret but mindlessly boring), I have to end writing Mindsport after this week. Okay, one reason is because of some prior writing commitments that are impossible to put off any longer. (I'll give you a hint: watch out for a film called Dream Sequence, which should be releasing around October; pay careful attention to the credits - and clap!)
Now, the good news. I'm going to leave you with two insanely difficult problems - you have up to the end of the year to solve. It's taken from a special IQ test, testing for IQs of 160 and above. The first one's answer is 6; the second I leave to you to solve. Have fun!
1. If a juggler juggles three different coloured objects, how many throws are necessary to return the objects to their starting positions if each object is thrown to the opposite hand at least once and a standard juggling pattern is used (ie: one hand throws an object, second hand throws an object, then the first, etc), and the juggler starts out with two objects in one hand (the first hand to throw an object) and one in the other?
2. Underline a famous mythical act of hero-ism: "Provide men the
use so toleration finds
residence free of misleading theories gift of decried species."

DEAR MS
(Problem 1: "In a 4x4 square grid, name the top left square A and top right square B. From A to B, what's the maximum number of squares a chess knight can touch, including A and B, if it makes only permissible moves, does not touch squares more than once and does not go outside the grid?" - MS)
Knight-In-Daze-Dept:
The knight will never reach from A to B. The maximum squares it can touch is 15 (including A), by making 14 moves.
- Saifuddin SF Khomosi, saif_sfk@hotmail.com

A knight can touch a maximum of 12 squares if it has to trot per rules and if it can't stray outside the 4x4 chess board. A board size of at least 4x5 squares is necessary if it has to touch all squares.
- Ramesh S Mahalingam, ramesh@idealmc.com
(Second: "A boiled egg and a raw egg start rolling down an endless ramp simultaneously. Which one leads and why?" - MS)

An- Eggsact-Solution-Dept:
The boiled egg will be in the lead as its mass is a solid, whereas the raw egg will roll slower due to its mass being fluid.
- Cader F Moosa,
caderfiras@gmail.com

Since the mass distribution in case of a boiled egg is uniform and the mass of a raw egg is concentrated on the circumference, the moment of inertia is more for the raw egg. It will, therefore, produce lesser angular acceleration as compared to the boiled egg (moment of inertia is inversely proportional to angular acceleration). And as linear acceleration is directly proportional to angular acceleration, the boiled egg will be ahead.
- Akshit, akshit0201@gmail.com

(Finally: "First list of five words: PRONE, VERSE, PALMIST, APRON, EVER. Second list of five words: PISTIL, PETAL, CALYX, SEPAL, ANTHER. Which word in the second list should come next in sequence as the sixth word in the first list?" - MS)

Potted-Parts-Dept:
SEPAL seems the simplest possible choice because if you remove the comma separating the words in the first list, EVER is the combination of E the last letter of PRONE and VER the next three letters after E. Similarly, SEPAL is the next word formed using SE from VERSE and the next three letters following SE. But APRON is formed using PRON from PRONE and the vowel A, which cannot be explained by the above logic. PISTIL can be explained by assuming that APRON is formed by combining the first vowel A with letters from PRONE and EVER by combining the second vowel E with letters from VERSE and PISTIL by combining I the third vowel with letters from PALMIST.
- Balagopalan Nair K,
balagopalannair@gmail.com
(This is the final instalment of Mindsport. To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)