Okay, so time for Round III of Talent Search Questions Last round was quite easy, all questions got answered in a night, so well done to everyone.
Let's see how you guys cope with these:
1. What are the last 2 digits of 6^2011 + 7^2011
2. Prove that a 10 x 10 chessboard can not be split up into 25 4x1 strips.
3. How many zeros are there at the end of 2011! ?
4. A company has 5 directors. Regulations of the company that any majority (3 or more) must be able to open its strongroom, but any minority (2 or less) of directors cannot. It is proposed that the door to the strongroom be equipped with 10 locks, so that when all ten locks are present, the door can be unlocked. Now each director is given a set of keys to exactly n doors, find all possible values of n such that there is a way to allocate the keys according to the regulations of the company.
5. Okay, this question is a mother of a question If anyone get's it correctly on their first attempt, I will be amazed at your amazingnessnessness (KK NO GOOGLING!!!)
Here goes: A magician has one hundred cards named 1 to 100. He divides them into 3 groups, and puts each group in separate boxes, boxes are coloured red, white and blue. Each box has at least one card in it.
A member of the audience then chooses 2 boxes, picks a card from each and announces the sum of the two cards. Given this sum, the magician identifies the box where no cards were taken.
Now the question is: How many ways are there to put all cards in the boxes so that this trick always works?
(Two ways are considered different if at least one card is put in a different box)
Hope these aren't too hard If you get stuck, here's a quick joke:
A statistician refuses to fly after reading that alarmingly high probabilities that of a bomb being on any given plane. But then a few weeks later he reads that the probability that 2 bombs are on any given plane is very low, so now when he flies, he carries a bomb with him at all times.
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Okay, so time for Round III of Talent Search Questions Last round was quite easy, all questions got answered in a night, so well done to everyone.
Let's see how you guys cope with these:
1. What are the last 2 digits of 6^2011 + 7^2011
2. Prove that a 10 x 10 chessboard can not be split up into 25 4x1 strips.
3. How many zeros are there at the end of 2011! ?
4. A company has 5 directors. Regulations of the company that any majority (3 or more) must be able to open its strongroom, but any minority (2 or less) of directors cannot. It is proposed that the door to the strongroom be equipped with 10 locks, so that when all ten locks are present, the door can be unlocked. Now each director is given a set of keys to exactly n doors, find all possible values of n such that there is a way to allocate the keys according to the regulations of the company.
5. Okay, this question is a mother of a question If anyone get's it correctly on their first attempt, I will be amazed at your amazingnessnessness (KK NO GOOGLING!!!)
Here goes: A magician has one hundred cards named 1 to 100. He divides them into 3 groups, and puts each group in separate boxes, boxes are coloured red, white and blue. Each box has at least one card in it.
A member of the audience then chooses 2 boxes, picks a card from each and announces the sum of the two cards. Given this sum, the magician identifies the box where no cards were taken.
Now the question is: How many ways are there to put all cards in the boxes so that this trick always works?
(Two ways are considered different if at least one card is put in a different box)
Hope these aren't too hard If you get stuck, here's a quick joke:
A statistician refuses to fly after reading that alarmingly high probabilities that of a bomb being on any given plane. But then a few weeks later he reads that the probability that 2 bombs are on any given plane is very low, so now when he flies, he carries a bomb with him at all times.
Edited by TwinhelixLink to comment
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