tag:blogger.com,1999:blog-35872402011-07-28T20:07:58.975-05:00A place for puzzlesLavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.comBlogger291100tag:blogger.com,1999:blog-3587240.post-12322586089427081902009-07-22T23:43:00.003-05:002009-07-22T23:47:29.510-05:00

Fair experiment with unfair coin!The puzzle is simple to state: You are given a biased coin with 60% chance for getting heads and 40% chance of getting tails while tossing. Design an experiment with two equally likely outcomes using the coin.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com1tag:blogger.com,1999:blog-3587240.post-75013956838232087822009-03-09T21:10:00.003-05:002009-03-09T21:18:14.330-05:00

Think out of the box!2 rooms, 1 light bulb in one room and the other room has 3 switches out of which only one of the light bulb switches on/off. The rooms are not viewable from each other. You as a single person has just one chance to find which switch operates the bulb. How can this be done?

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com2tag:blogger.com,1999:blog-3587240.post-69101623113737721532008-12-22T22:04:00.002-06:002008-12-22T22:13:24.113-06:00

An Interval GraphSix professors had been to the library on the day when the rare tractate was stolen. Each had entered once, stayed for some time and then left. If two were in the library at the same time, then at least one of them saw the other. Detectives questioned the professors and gathered the following testimony:A said he saw B and EB reported he saw A and IC claimed he saw D and ID said

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-46019200854493324692007-03-06T15:31:00.000-06:002007-03-06T15:34:26.467-06:00

Unit distance coloringImagine that each point on the plane takes a color. What is the minimum number of colors needed to color all the points so that any two points which are at distance exactly 1 unit get two different colors?

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1124242407621141222005-08-16T20:28:00.000-05:002005-08-16T20:33:27.626-05:00

The Plane in the WindAn airplane flies in a straight line from airport A to airport B, then back in a straight line from B to A. It traverses with a constant engine speed and there is no wind. Will its travel time for the same round trip be greater, less, or the same if, throughout both flights, at the same engine speed, a costant wind blows from A to B?

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1120494937916187312005-07-04T11:20:00.000-05:002005-07-04T11:35:37.946-05:00

Back with a bang :)Manupulative codewords - Hofstadter's MIU system This system of codewords have only stings of letters formed from the alphabets, M, I, U with MI as one of the codewords. You can form other codewords in the system by the following four rules :x in the below lines can be any string of letters from M, I, U that makes a codeword in each of the rules.<!-- MATH $xI\in \mathcal{T}$

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com1tag:blogger.com,1999:blog-3587240.post-1059683021346729682003-07-31T15:23:00.000-05:002005-07-27T11:02:07.400-05:00

Students in the LibraryFive students visited the library on a certain day. The library is open from 8 AM - 8 PM on all days. Each went for a lunch at some time and returned after it. Any two of them met in the library. Prove that at some moment of time three of them were in the library. Show also that this is not always true for four students.Hint (posted on July 27, 2005): Draw interval lines

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.comtag:blogger.com,1999:blog-3587240.post-1058721529229707272003-07-20T12:18:00.000-05:002003-07-20T12:18:49.186-05:00

Girlie company 25 boys and 25 girls are to be seated in a round table with 50 seats. Prove that no matter what the arrangement is, there would be a person who is seated in-between two girls.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1058534534068806072003-07-18T08:22:00.000-05:002003-07-18T08:23:20.096-05:00

The hole principle Let A = (a_1, a_2,...,a_n) be a sequence on real numbers with n > k m (k and m - integers). Prove that there is a subsequence of length k +1 of A of which is increasing OR a subsequence of length m +1 of A of which is decreasing.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1057440536609821052003-07-05T16:28:00.000-05:002003-07-05T18:03:42.210-05:00

A non-rational path Consider R^2 - the Euclidean plane consisting of 2-tuples of real numbers. Remove all the points that have rational co-ordinates from it. For example (1/4, 5/100) should be removed, (1/2, sqrt(7)) should NOT be removed. We are left with what is denoted R^2 - Q^2; Q being the rational points. Pick any two points a and b in R^2 - Q^2. Is it possible to find a path (a line -

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1057289315213998912003-07-03T22:28:00.000-05:002003-07-04T15:35:20.696-05:00

Count the sum of the determinants To each positive integer with n^2 number of digits, we can associate a corresponding determinant by writing the digits in order across the rows. That is for n = 2, we have n^2 = 4. Thus take all 4-digit positive integers. For 7615, we have the determinant | 7 6 | | 1 5 | which is equal to 35 - 6 = 29. Can you find the sum of all determinants associated

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-1057275078127790372003-07-03T18:31:00.000-05:002003-07-03T18:31:18.076-05:00

A computational Problem Let x = .1234567891011121314...998999, where the digits are obtained by writing the integers 1 through 999 in order. Find the 1983rd digit to the right of the decimal point.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-819367952002-09-21T22:41:00.000-05:002003-03-25T21:19:23.000-06:00

Can the mouse eat the cube? A mouse eats its way through a 3*3*3 cube of cheese by tunnelling through all of the 27 1*1*1 subcubes. If he starts at one corner and always moves on to an adjacent uneaten subcube, can he finish at the center of the cube?

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-815051742002-09-12T08:45:00.000-05:002002-09-12T08:45:25.376-05:00

More on Primes Prove that there is atleast one prime number between n and 2n.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-812986882002-09-07T21:32:00.000-05:002002-09-07T21:32:51.250-05:00

Consecutive no-prime numbers Tell me 1000 consecutive non-prime numbers.

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-812158682002-09-05T21:00:00.000-05:002002-09-06T18:48:47.000-05:00

I am not naming this! Well, I name it Handshakes At a recent convention of Scientists, there was a lot of handshakes between the scientists. But the number of Mathematicians in attendence who shook hands an odd number of times was even, why?! Remember that an handshake requires exactly two different people!

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-811203902002-09-03T21:31:00.000-05:002002-09-03T21:31:47.530-05:00

The Frog and the Wall Suppose there is a frog at a certain distance from a wall, say, ten feet. Imagine that this frog jumps halfway to the wall, so that he is five feet away. Suppose he continues to jump toward the wall, each time getting halfway there. Will the frog reach the wall? Another Question will follow in this context!

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-804318212002-08-19T10:41:00.000-05:002002-08-19T10:44:38.000-05:00

The Structure of the Universe We say that space is three-dimensional. But in the world of Mathematics, though, we are not limited by physical constraints!! We might have four, five, or six geometric dimensions, or even infinitely many!!! Let's go back to two-space. Thos might be a plane or the surface of a smooth objects. Suppose we have little cretures on this two-dimensional surface. Their

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-802611792002-08-14T23:11:00.000-05:002002-08-14T23:13:31.000-05:00

Tricky Track Three High schools-Washington, Lincoln and Roosevelt-competed in a track meet. Each school entered one man, and one only, in each event. Susan, a student of Lincoln High, sat in the bleachers to cheer her boyfriend, the school's shot-put champion. When Susan returned home later in the day, her father asked how her school had done. "We won the shot-put all right," she said,"but

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-801910992002-08-13T11:50:00.000-05:002002-08-13T11:55:30.000-05:00

The Twin Paradox This blog is as a result of my own attempt to understand a difficult-to-understand paradox, Twin Paradox which is an outcome of of Einstein's relativity (Any physicians around?!). Please tell me if you see anything insightful!(I have question-marked whatever I did not understand!) Suppose we have two twin brothers, in spaceships somewhere in the intergalactic void where there

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-800353682002-08-09T13:05:00.000-05:002002-08-09T18:30:43.000-05:00

A Band Around The World Suppose the earth were a smooth, perfectly round sphere, with no hills or mountains. Imagine a rope around the earth's equator, strung so that it is snug and does not strech. If we were to add, say, ten feet to this rope, and then prop it up all the way around the planet so that it stood out equally far everywhere, how far above the surface would it stand? We can assume

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-798352582002-08-05T01:24:00.000-05:002002-08-05T01:35:43.000-05:00

A Fixed-Point Theorem One Morning, exactly at sunrise, a Buddhist monk began to climb a tall mountain. The narrow path, no more than a foot or two wide, spiraled around the mountain to a glittering temple at the summit. The monk ascended the path at varying rates of speed, stopping many times along the way to rest and to eat the dried fruit he carried with him.He reached the temple shortly before

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com1tag:blogger.com,1999:blog-3587240.post-794560162002-07-26T17:53:00.000-05:002002-07-27T00:20:10.000-05:00

The Car-and-Goats II This is a continuation of the previous question... If the car is actually at Door I (probability 1/3), then when you switch you lose; but if it is at Door 2 or Door 3(probability 2/3) then the host's revelation of a goat shows you how to switch and win. Therefore the chance you win by switching is 2/3. Elegant. But in this argument, we are still considering the possibility

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-793912282002-07-25T08:34:00.000-05:002002-08-05T01:34:49.000-05:00

The Car-and-Goats A number of mathematicians were thrown into a tizzy by the following problem, which appeared in Marilyn vos Savant's column, "Ask Marilyn", in Parade(a Sunday newspaper supplement): One of the three doors hides a car (all three equally likely) and other two hide goats. You choose Door 1. The host, who knows where the car is, then opens one of the other two doors to reveal a goat

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-786471792002-07-07T08:15:00.000-05:002002-08-05T01:36:40.000-05:00

Random Hats Three people are given hats. Each hat is either red or blue, chosen at random. Each person can see the other 2 hats, but not their own. They each must simultaneously either guess their own hat's color, or pass. No communication is allowed, although they can agree on a strategy ahead of time. What strategy will give them the best chances of at least one person guessing right, and

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-785233552002-07-03T16:12:00.000-05:002002-08-05T01:37:26.000-05:00

Probability While your back is turned, a friend places a penny, nickel, and dime on the table. He arranges them in a pattern of heads and tails provided that the three coins are not all heads or all tails. Your object is to give instructions, without seeing the coins, that will cause all heads to be the same (all heads or all tails). For example, you may ask your friend to reverse the dime. He

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-780113892002-06-20T23:40:00.000-05:002002-07-27T00:37:51.000-05:00

Guess the numbers Two mathematicians are placed in two rooms and one is given the sum of two distinct numbers between 2 and 99 (2 and 99 excluded) and the other is given the product of same two numbers. They both come out of the room and the following conversation takes place. Mathematician with product : "I don't know the two numbers". Mathematician with sum : "I know, you won't know the two

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-779838262002-06-20T11:12:00.000-05:002002-06-20T11:12:04.830-05:00

Hi there, I installed YACCS, so you can comment!

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0tag:blogger.com,1999:blog-3587240.post-779801032002-06-20T09:32:00.000-05:002002-06-20T11:06:06.000-05:00

Mirror, Mirror... I found this problem in "No Ordinary Genius" by Christopher Sykes. It's pretty easy. But I do not have an answer! You look in a mirror, and let's say you part your hair on the right side. You look in the mirror, and your image has its hair parted on the left side, so the image is left-to-right mixed up. But it's not top-to-bottom mixed up, because the top of the head of the

Lavanyahttp://www.blogger.com/profile/14123070597007673219noreply@blogger.com0