1. P

    Probablity - round table

    How many ways there is when sitting next to round table of n-chairs? How many ways there is if Dan and David don't want to sit together? What is the formula?
  2. N

    Which way round should I answer this question.

    Question Find the range of values of M for which the line y=mx-5 intersects the curve y=x^2-4x+5 in two distinct points. I completed the question by integrating the linear into the quadratic and then solved by doing the discriminant. I have the 2 answers as -6 and -2 I'm just unsure whether...
  3. J

    Round Robin Voting System

    Hey guys, How would I create a round-robin voting system that takes any number of creators, all submitting products to be voted on by each other, and produces a unanimous result within a given timescale of eg. 1 week? Each user both submits their work and votes on their peers work (voting is...
  4. W

    2012 HMMT November - Guts Round

    I just participated in this tournament, note: the questions are fairly hard, do not feel bad if you could not solve some of them, and actually, if you could solve more than half of those, you are already amazing! The rules: work 3 at a time, after you hand in the 3 questions you were working...
  5. T

    Surface area of Rectangular / Round transition

    Hello, This is my first post on this forum. I am creating an excel spreadsheet that will calculate me the weights of sheet metal HVAC ductwork and I am creating the equations for weight myself. I have some equations which I cannot figure out. For calculation of weight I need the surface area...
  6. P

    No. of ways to seat round a table (numbered seats)

    Two families are at a party. The first family consists of a man and both his parents while the second familly consists of a woman and both her parents. The two families sit at a round table with two other men and two other women. Find the number of possible arrangements if the members of the...
  7. J

    USAMTS round 2 problem (2004-2005)

    3/2/16. A set is reciprocally whole if its elements are distinct integers greater than 1 and the sum of the reciprocals of all those elements is exactly 1. Find a set S, as small as possible, that contains two reciprocally whole subsets, I and J, which are distinct but not necessarily disjoint...
  8. J

    USAMTS round 2 problem (2006-2007)

    1/2/18. Find all positive integers n such that the sum of the squares of the digits of n is 2006 less than n.
  9. J

    USAMTS round 1 problem (2006-2007)

    1/1/18. When we perform a ‘digit slide’ on a number, we move its units digit to the front of the number. For example, the result of a ‘digit slide’ on 6471 is 1647. What is the smallest positive integer with 4 as its units digit such that the result of a ‘digit slide’ on the number equals 4...
  10. J

    USAMTS round 3 problem (2006-2007)

    Find, with proof, all real numbers x between 0 and 2\pi such that tan7x-sin6x = cos4x-cot7x.
  11. J

    USAMTS round 1 problem (2004-2005)

    2/1/16. For the equation (3x^2+y^2-4y-17)^3-(2x^2+2y^2-4y-6)^3 = (x^2-y^2-11)^3, determine its solutions (x, y) where both x and y are integers. Prove that your answer lists all the integer solutions.
  12. T

    In how many ways can 5 men and 5 women sit at a round table

    In how many ways can 5 men and 5 women sit at a round table such that no two persons of the same gender sit next to each other?