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Showing posts from November, 2011

### 21 Problems in 21 Days left for Placements

For 21 days left for IIT placements, Siddhant Agarwal (EE IITB 2011 Alumnus, CMI Grad student) and Vivek Jha (EE IITB 2011 Alumnus, Credit Suisse Analyst) have selected 21 problems out of ~200 problems on the blog, so that people can prepare for the placements in the last minute. Help yourself! Cheers! Best of Luck! Locks and Switches The Best Horse Duplicate Integer Stick Broken Into Three Pieces Finding a hermit Prime Number Strategy Game Hats and Rooms Need for Needles Checkers Problem King's Poisonous Wine II Smallest Number in Decreasing Sequence Increasing Sequence in Dice Random point in a circle Another Coin Problem Painting Colored Balls Another Hat Problem Arrange in a Sequence Russian Coins Top Card Ants on a Cube Coin Balancing

### Guess 3 numbers

Source : Quantnet Forums Problem : A question which is asked on interview in some software development companies. I guessed 3 natural numbers - x,y,z. You can ask me about two sums of these numbers with any coefficients - a,b,c. For example, you give me a, b and c and I tell you the result of the expression a*x+b*y+c*z. Give me the algorithm to find x,y and z. Observation/Hint : Irrespective of whether you get the solution, its interesting that you are solving a system of three variables using two equations. You are able to do that because the coefficient in the second equation depends on the answer of the first equation. :) Update (November 6, 2011): Solution : Posted by Harsh Pareek (Graduate Student at UT Austin, CSE IITB 2011 Alumnus), Rudradev Basak (IITD CSE Senior Undergraduate) and AnonymousD in comments!

### Scaling a Square

Source : Saurabh Joshi, IIT Kanpur Problem : On a table you have a square made of 4 coins at the corner at distance 1. So, the square is of size 1×1. In a valid move, you can choose any two coin let’s call them mirror and jumper. Now, you move the jumper in a new position which is its mirror image with respect to mirror. That is, imagine that mirror is a centre of a circle and the jumper is on the periphery. You move the jumper to a diagonally opposite point on that circle. With any number of valid moves, can you form a square of size 2×2? If yes, how? If no, why not? Update (November 4, 2011) Solution : Posted by Siddhant Agarwal (EE IITB Alumnus, CMI Grad student) and Rudradev Basak (IITD CSE Senior Undergraduate) in comments!

### Divisibility of 111...1111

Source : Asked to Russian 7th Graders - Taken from Wild For Math Blog Problem : Is it true that among the numbers consisting of only "1"s (1; 11; 111; 1111; etc.) there is a number (maybe many) that is divisible by 572,003? Here 572,003 is taken arbitrarily. Is it true for all numbers? Update (November 02, 2011): Solution posted in comments by NG a.k.a Nikhil Garg (IITD CSE Senior Undergraduate), Rudradev Basak (IITD CSE Senior Undergraduate, IMO Bronze Medalist), Yashoteja Prabhu (RA at Microsoft Research, IITB CSE 2011 Alumnus), Siva, Garvit Juniwal (IITB CSE Senior Undergraduate)! Thanks