'No' Denying The Question

All you have to do is predict whether or not the event will happen by pressing a 'YES' or 'NO' button.

E4
Let's see if you can work this out. Supposing you're told that an event that may or may not happen in the next five minutes has been written on a piece of paper. For example, it might be written that the person nearest to you is going to cough in the next five minutes. Equally, it might be written that the world is going to end in the next five minutes. It could be anything. All you have to do is predict whether or not the event will happen by pressing a 'YES' or 'NO' button. If you're correct, you're told you'll be given a thousand bucks. Also, after you make your choice, the piece of paper will immediately be shown to you.
So, you think that you and a friend could each press a YES and NO button and since one of you HAS to win, you'll share the money, right? In which case, what if what is written on the piece of paper is "You will press the NO button". How come you both lost?
(Incidentally, here's something similar: A man who is on death row is given an option to choose his mode of death. He is asked to make a statement. If the statement he makes is true, he will be hung; if it is false, he will be shot. The convict however messes it all up by saying: "I'm going to be shot.")
DEAR MS
(The overnighter was about manually weighing pre-bagged oranges and the question was: "How many bags will you have to pick up to be 85 per cent certain you're not being cheated if the number of bags to choose from was large and there were no bags whose weight was equal to the median? - MS)
In-The-Bag Dept:
This problem can also be interpreted as the minimum number of bags needed to be checked so that the probability of being cheated is less than 15 per cent. Now, for the first two bags the probability of being cheated is p(2) = 0.25 + 0.5*0.1 = 0.3. For every subsequent bag checked the probability p(n) of being cheated is p(n) = (0.5 + 0.1*0.5)*p(n - 1) = 0.55p(n - 1). Now we have to find minimum "n" such that p(n) < 0.15. Hence we have n = 4. Thus four bags need to be checked before the customer is 85 per cent sure of not being cheated.

• Alan D'Souza, iamaland@gmail.com
  

(The other problem concerned A and B digging holes where, after a few given conditions, you had to calculate how long did A dig for. - MS)
Hole-In-One Dept:
Thoroughly enjoyed cracking this one ! The answer is: A dug for 39 minutes. If we take a as the height of A (in inches) and b as the height of B (in inches), then 6a = 7b. Also, ax - b(x - 2) = A; and b(x - 2) = B. Solving these equations and keeping in mind that A and B are shorter than 84" and everything is integral and that b < a, we get x = 39.

• Saifuddin S F Khomosi, saif_sfk@hotmail.com
  

(The third problem was: "??, EN, SU, NR, RE, SR, ??, SU, YR." - MS)
All-In-The-Stars Dept:
The answer is HT from the planet where we all live - EARTH. The letters are the last two letters of the planets in the solar system, written in reverse and in decreasing distance from the Sun. Neptune (EN), Uranus (SU), Saturn (NR), Jupiter (RE), Mars (SR), Earth (HT), Venus (SU) and Mercury (YR).

• Sheikh Sintha Mathar, sheikhsm7@gmail.com
  

ENDGAME(S)

1. Seven robbers steal some diamonds. At night, two of them wake up and decide to split the loot. But there's one extra diamond. They wake up a third robber to distribute it into three parts. There's still one diamond extra. So is the case with the 4^th, 5^th and 6^th robber. But, when they divide the diamonds into seven parts, they get equal parts. What is the least number of diamonds to make the situation true? - Submitted by Aaditya Shankar Natarajan, aaditya.shankar.n@gmail.com
2. 527F in Celsius is 275; in other words, same number with the first digit shifted to the last position. What is the next lowest temperature with this property?

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

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