• Probability in a square pyramide?

    In the following question http://answers.yahoo.com/question/index?qid=20130510121304AAXndU3 just replace a cone C with a pyramide P with square base. Again the question is to determine the probability that by picking 3 points randomly in P, the corresponding squares have pairwise non-empty intersections. I expect the answer to be slightly... show more
    In the following question http://answers.yahoo.com/question/index?... just replace a cone C with a pyramide P with square base. Again the question is to determine the probability that by picking 3 points randomly in P, the corresponding squares have pairwise non-empty intersections. I expect the answer to be slightly smaller than in the cone version, which has been estimated to be around 0.115 I am interested in theoretical or numerical answers.
    1 answer · Mathematics · 6 years ago
  • Drawing card question, any guess?

    Suppose you take the spades out of a game of cards and pick them at random while calling "Ace, King" etc down to 2 in that order. The probability that your call never agrees with the drawn card is a number P close to 1/e. http://mathworld.wolfram.com/Derangement.html Suppose you take the Spades and the Clubs and you draw them while... show more
    Suppose you take the spades out of a game of cards and pick them at random while calling "Ace, King" etc down to 2 in that order. The probability that your call never agrees with the drawn card is a number P close to 1/e. http://mathworld.wolfram.com/Derangement... Suppose you take the Spades and the Clubs and you draw them while calling "Ace King"... down to two, twice in a row. Then the probability Q of having only miscalls should be close to P^2. Can you find some heuristic argument to guess whether Q will be greater, less than or equal to P^2?
    5 answers · Mathematics · 6 years ago
  • Which numbers N can be written as pq(p+q) with p<q, in at least two different ways?

    N,p,q are nonnegative integers. N = 30 is the smallest solution. Is there a way to find all others?
    N,p,q are nonnegative integers. N = 30 is the smallest solution. Is there a way to find all others?
    2 answers · Mathematics · 6 years ago
  • Probability in a cone, numerical or theoretical answers welcome?

    Consider the cone C over the unit disk D defined in R^3 by z > 0 and x^2+y^2 <= (1-z)^2. Each point (u,v,r) in C defines a disc of center (u,v) and radius r included in D. The question is to determine the probability that by picking 3 points randomly in C, the corresponding disks have pairwise non-empty... show more
    Consider the cone C over the unit disk D defined in R^3 by z > 0 and x^2+y^2 <= (1-z)^2. Each point (u,v,r) in C defines a disc of center (u,v) and radius r included in D. The question is to determine the probability that by picking 3 points randomly in C, the corresponding disks have pairwise non-empty intersections. "Randomly in C" means "uniformly with respect to the Lebesgue measure" normalised by the volume of the cone namely pi / 3.
    3 answers · Mathematics · 6 years ago
  • Can you find the largest integer N with the following property?

    Let S consist of any set of 10 distinct positive integers that are all less or equal than N. Prove that there will always exist at least two subsets of S whose elements sum to the same number. Inspired by http://answers.yahoo.com/question/index;... where it is shown that N is at least 100.
    Let S consist of any set of 10 distinct positive integers that are all less or equal than N. Prove that there will always exist at least two subsets of S whose elements sum to the same number. Inspired by http://answers.yahoo.com/question/index;... where it is shown that N is at least 100.
    3 answers · Mathematics · 6 years ago
  • Let "phi" be the golden mean. Can you show that 0 < (phi^2) /5 - (pi/6) < 10^(-5)?

    That is.... without a calculator.... This is related to the length of the royal cubit.
    That is.... without a calculator.... This is related to the length of the royal cubit.
    4 answers · Mathematics · 6 years ago
  • Like number theory problems?

    Let A be an even integer such that A^2 + 1 be composite. Can you always find (a,b) integers with b odd, such that a^2+b^2 = A^2+1, and 10*b > A. Related to http://answers.yahoo.com/question/index;... If not, counterexamples welcome, smallest wins...
    Let A be an even integer such that A^2 + 1 be composite. Can you always find (a,b) integers with b odd, such that a^2+b^2 = A^2+1, and 10*b > A. Related to http://answers.yahoo.com/question/index;... If not, counterexamples welcome, smallest wins...
    2 answers · Mathematics · 6 years ago
  • Geometry in the circle.?

    Let PQRS a quadrilateral inscribed in a circle C. Let I be the middle of PR and J be the middle of QS. Suppose the line QI intersects C at Q and Q' and RJ intersects C at R and R'. Show that if SQ' is parallel to PR then PR' is parallel to QS. This is a rewording of : http://answers.yahoo.com/question/index;...
    Let PQRS a quadrilateral inscribed in a circle C. Let I be the middle of PR and J be the middle of QS. Suppose the line QI intersects C at Q and Q' and RJ intersects C at R and R'. Show that if SQ' is parallel to PR then PR' is parallel to QS. This is a rewording of : http://answers.yahoo.com/question/index;...
    5 answers · Mathematics · 6 years ago
  • Prove CosA/CosB + CosB/CosC +CosC/CosA + 8 CosA CosB CosC ≥ 4.?

    Here ABC is an acute triangle. A similar inequality was asked not long ago. http://answers.yahoo.com/question/index;... This one seems harder. I only have computer evidence of its validity.
    Here ABC is an acute triangle. A similar inequality was asked not long ago. http://answers.yahoo.com/question/index;... This one seems harder. I only have computer evidence of its validity.
    4 answers · Mathematics · 6 years ago
  • Can you find the next terms of 1,2,4,7,12,19,30,45,67,97,139....?

    If you set a_0 = 1, a_1 = 2 etc, then a_k is the number of integer solutions of x + 2y + 3v + .......+ <= k.
    If you set a_0 = 1, a_1 = 2 etc, then a_k is the number of integer solutions of x + 2y + 3v + .......+ <= k.
    2 answers · Mathematics · 7 years ago
  • Can one split the 81 first squares into 9 groups of 9 squares each with identical sum?

    The sum of the all the squares up to 81^2 is 81*82*163/6 = 180441 so that the sum in each group would be 20049. Algebraic solution preferred. Thx
    The sum of the all the squares up to 81^2 is 81*82*163/6 = 180441 so that the sum in each group would be 20049. Algebraic solution preferred. Thx
    7 answers · Mathematics · 7 years ago
  • Circles in geometric progression, tangency problem II?

    Circles are in geometric progression if their radii R_n are in geometric progression R_n = a r^n with r not equal to 1, and their centers can be isometrically mapped on the complex plane so that their images z_n, are also in geometric progression z_n = b z^n with b in C and |z| = r so that the sequence is self-similar. The question is: what is... show more
    Circles are in geometric progression if their radii R_n are in geometric progression R_n = a r^n with r not equal to 1, and their centers can be isometrically mapped on the complex plane so that their images z_n, are also in geometric progression z_n = b z^n with b in C and |z| = r so that the sequence is self-similar. The question is: what is the maximum length of a geometric sub-sequence of circles such that there exists a circle (not in the sequence) tangent to all of them? Follow up from http://in.answers.yahoo.com/question/ind...
    1 answer · Mathematics · 7 years ago
  • Tangent circles in geometric progression.?

    Circles are in geometric progression if their radii R_n are in geometric progression R_n =r^n with r not equal to 1, and their centers can be isometrically mapped on the complex plane so that their images z_n, are also in geometric progression z_n = z^n. The question is: what is the maximum length of a geometric sequence of circles such that... show more
    Circles are in geometric progression if their radii R_n are in geometric progression R_n =r^n with r not equal to 1, and their centers can be isometrically mapped on the complex plane so that their images z_n, are also in geometric progression z_n = z^n. The question is: what is the maximum length of a geometric sequence of circles such that there exists a circle (not in the sequence) tangent to all of them.
    2 answers · Mathematics · 7 years ago
  • Finite sets and parts. For which integers N is the following possible?

    Start with E a set with N elements. You want N subsets A_1,...,A_N of same cardinal k, whose union is E and such that pairwise intersections consist of exactly one element of E for all A_i, A_j, For N = 3: E = {a,b,c} you can take {a,b} {b,c} {c,a} For which integers N is this possible? http://in.answers.yahoo.com/question/ind...
    Start with E a set with N elements. You want N subsets A_1,...,A_N of same cardinal k, whose union is E and such that pairwise intersections consist of exactly one element of E for all A_i, A_j, For N = 3: E = {a,b,c} you can take {a,b} {b,c} {c,a} For which integers N is this possible? http://in.answers.yahoo.com/question/ind...
    3 answers · Mathematics · 7 years ago
  • Permutations problem?

    For which values of N can you find a permutation (a0, a1, a2.....aN) of numbers 0-N such that (a0, |a1-1|,|a2-2|,...|aN-N|) is also a permutation? http://in.answers.yahoo.com/question/ind...
    For which values of N can you find a permutation (a0, a1, a2.....aN) of numbers 0-N such that (a0, |a1-1|,|a2-2|,...|aN-N|) is also a permutation? http://in.answers.yahoo.com/question/ind...
    4 answers · Mathematics · 7 years ago
  • Quadrilaterals with integer sides and square integers.?

    Consider quadrilaterals ABCD with integer sides all different, area and perimeters both square integers. ABCD is convex with 2 right angles in B and D. How many such quadrilaterals are there assuming that the smallest side has length 1: none, finitely many or infinitely many? From the answers... show more
    Consider quadrilaterals ABCD with integer sides all different, area and perimeters both square integers. ABCD is convex with 2 right angles in B and D. How many such quadrilaterals are there assuming that the smallest side has length 1: none, finitely many or infinitely many? From the answers in http://in.answers.yahoo.com/question/ind... you see that the smallest side can be 5.
    3 answers · Mathematics · 8 years ago