Dinner Table Conundrum

E4
Know something? Lewis Carroll (he of the Alice's Adventures in Wonderland fame) is in good company. He too used to write a column like Mindsport in The Monthly Packet from April 1880 onwards for a number of years. And guess what else? He also used to get a lot of mail - although nothing compared to the cache we receive here. Thus, I was vastly relieved to discover that at least in that one department we remain streets ahead. Meaning, don't you dare discontinue your heartfelt barrage lest we fall short of professor Charles Lutwidge Dodgson (he of Euclid and his Modern Rivals fame)! Meanwhile, here's an original puzzle of his that appeared more than a hundred years ago:
"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. Find the number of guests."
 
DEAR MS
(The problem was: "A ladder is leaning on a wall [which is perpendicular to the floor]. It is initially at rest. Now it starts to slide down [there is no friction]. Prove that the ladder loses contact with the wall when it slides down exactly 1/3rd of its original height." - MS)
 
Up-The-Down-Staircase-Dept:
For a ladder of length L sliding down in contact with the wall, its centre of mass moves in a circle of radius L/2. We have to determine the position at which the horizontal centre of mass speed starts to decrease. Since the normal force cannot be negative, this is the point where the ladder loses contact with the wall. If 'A' is the angle between the ladder and the wall, using conservation of energy and letting the moment of inertia of the ladder =  . . . (Lots of calculations here involving cosines and stuff which no normal human needs to involve him or herself with - MS) . . . Using calculus, we find that the horizontal speed is the maximum when cosA = 2/3. Therefore, the ladder loses contact with the wall when it slides down exactly 1/3rd of its original height.
- Saifuddin Khomosi, saif_sfk@hotmail.com
 
(The second was: "Two pilots starting from a place flew away from each other. After some time, they found they were approaching each other. Stranger still, at the start, when they were separating from each other and also at the end, when they were approaching each other, they were both moving in the same direction. How?" - MS)
 
Plane-Solutions-Dept:
A general solution would be planes taking off in the same direction but with different accelerations at any point on the Earth. The plane having the higher acceleration will move forward from the other one. Now, if during flight, acceleration is reversed (higher one gets lowered acceleration), then it could happen that while ending the flight, the planes may approach each other and still be moving in the same direction.
- Altaf Ahmed, ctrlaltaf@yahoo.in
 
(The third was, why on winning a Canadian lottery one is also asked a trivia question before getting the money. - MS)
 
Big-Moolah-Dept:
In Canada, if you win a lottery, you have to answer a "Skill Testing Question". It all has to do with laws, and loopholes. The Canadian Competition Act bans all games of chance. Contest officials figured out if they require a correct answer to a tricky question as part of their entry, their sweepstake is no longer considered a game of chance.
- Jaelyne Tauro, jaelynetauro@gmail.com
 
ENDGAME(S)
1. A stone thrown in a lake produces round concentric waves. What form will the waves take if a stone is thrown in a flowing river?
2. 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. If the ages are in whole years, how old are they now?

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

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