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All Hands On Deck

There are basically two ways to solve this seemingly impossible problem. After all you're blindfolded for crying out loud, so how can you even make out the cards, right?

By Mukul Sharma

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Published: Thu 3 Dec 2015, 11:00 PM

Last updated: Fri 4 Dec 2015, 8:22 AM

E4
Want to know how to win friends and un-fluence people? Here's what you have to do: Tell someone to take an ordinary pack of cards and turn any number of them face up in the deck and anywhere they want to without you seeing or knowing it. All they have to do is tell you how many have been face-upped (FU). Now enter with a flourish of trombones and declare that on knowing the number of FUs in the pile of cards lying in front you can sort the cards into two groups, such that each group contains the same number of FU cards.
Then brace hard for some raucous denigrating laughter as the collective hordes of non-Houdinis around you snap at your jugular saying any idiot could do the same with nary a flip of an eyelid. <That's> when you come into your own. Rising three feet taller than what you are in actual stature, you proclaim that you're going to do it blindfolded! Yessiree - blind-freaking-folded! Then, as several pins start to drop around you to shatter the sudden silence on the floor, show them how. (Of course if you know how, that is.) (Do you?)
There are basically two ways to solve this seemingly impossible problem. After all you're blindfolded for crying out loud, so how can you even make out the cards, right? The first method is by using high-end mathematics which would give an algebraic solution; and the second is by using low end brains and lots of logic, which would nevertheless yield a surprisingly elegant solution. Take your pick.
DEAR MS
(The problem was: "A digital clock shows both time and date in the format hh:mm:ss and month/day. It is a 24-hour clock (times range from 00:00:00 to 23:59:59) and leading zeros are allowed. If all 10 digits 0 to 9 appear on the display, what is (a) the earliest, and (b) the latest date and time in the year this could happen?" - MS)
Time-Of-The-Year Dept:
The earliest time of the year this can happen is at 17:48:59 03/26 and the latest time of the year would be at 17:56:43 09/28. - Saifuddin S F Khomosi, saif_sfk@hotmail.com
(The other problem was about a hole through the Earth from pole to pole and a car falling frictionless through it. Seven questiona regarding its velocity, acceleration, weight, etc, were asked including if a cigarette could be smoked inside it. - MS)
Pole-Position Dept:
Regarding the hole through the Earth problem, anyone who did high school science and read a chapter on gravitation could give you the right answers. (1) Velocity increases. (2) Acceleration increases till the centre. (3) Spring balance will weigh less than on the Earth's surface. (4) Gravitation force will be zero at the Earth's centre. But since we are going to be in a state of free fall during the journey we would experience zero gravity during the whole trip. Force must not be equated to the feeling of force. (5) Velocity will be maximum at the Earth's centre with a value around 7.9*10^3m/s. (6) We can't smoke in free fall condition as the smoke will not go upwards (7) Time will be 3.14(R^3/GM)^(1/2). - Alan D'Souza, iamaland@gmail.com
(Clarification is needed on question #6: namely, could one smoke inside the car? Cigarettes won't stay lit in zero-g unless one constantly waves them about. Gases produced by the burning of tobacco must be carried upwards by the buoyancy of air, in turn caused by gravity pulling air down. - MS)
ENDGAME(S) 
1. A man is looking at a portrait when a passerby asks him, "Whose picture are you looking at?" The man replies: "Brothers and sisters have I none, but this man's father is my father's son." So whose picture was he looking at?
2. Of those numbers whose English representation in capital letters consists only of straight lines, only one number has a value equal to the number of straight line segments required to write it out. What number is it?
(To get in touch with Mukul, mail him at mukul.mindsport@gmail.com)


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