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gianlino
I often give sketchy answers, but if the gaps are too wide email me.
Probability in a square pyramide?
In the following question
http://answers.yahoo.com/question/index?qid=201305...
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 AnswerMathematics8 years agoDrawing 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 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 AnswersMathematics8 years agoWhich 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?
2 AnswersMathematics8 years agoProbability 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 intersections.
"Randomly in C" means "uniformly with respect to the Lebesgue measure" normalised by the volume of the cone namely pi / 3.
3 AnswersMathematics8 years agoCan 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;%E2%80%A6
where it is shown that N is at least 100.
3 AnswersMathematics8 years agoLet "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.
4 AnswersMathematics8 years agoLike 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;_ylt=AqKV8...
If not, counterexamples welcome, smallest wins...
2 AnswersMathematics8 years agoFor p = 2q+1 odd prime, 2^q = 1 mod p iff p = +- 1 mod 8. True or false?
This q originates from
3 AnswersMathematics8 years agoGeometry 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 :
5 AnswersMathematics8 years agoProve 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;_ylt=AoNIl...
This one seems harder. I only have computer evidence of its validity.
4 AnswersMathematics8 years agoDefinition please: what is an export price?
1 AnswerCorporations9 years agoDefinition please: what is an export price?
1 AnswerEconomics9 years agoCan 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.
2 AnswersMathematics9 years agoCan 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
7 AnswersMathematics9 years agoWhat are the integer solutions of x^2 -2 = 2 y^3?
6 AnswersMathematics9 years agoCircles 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 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
1 AnswerMathematics9 years agoTangent 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 there exists a circle (not in the sequence) tangent to all of them.
2 AnswersMathematics9 years agoFinite 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?
3 AnswersMathematics9 years agoPermutations 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?
4 AnswersMathematics10 years agoQuadrilaterals 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 in
http://in.answers.yahoo.com/question/index;_ylt=Ai...
you see that the smallest side can be 5.
3 AnswersMathematics10 years ago