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Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

The probability of getting at least one "6" in four rolls of a single 6-sided die is 1-(5/6)^4 approx 0.5177, (1) which is slightly higher than the probability of at least ...

Find necessary and sufficient conditions that determine when the integral curve of two periodic functions kappa(s) and tau(s) with the same period L is a closed curve.

A necessary and sufficient condition that there should exist at least one nondecreasing function alpha(t) such that mu_n=int_(-infty)^inftyt^ndalpha(t) for n=0, 1, 2, ..., ...

The resultant of the vectors represented by the three radii from the center of a triangle's circumcircle to its polygon vertices is the segment extending from the ...

For 2<=n<=32, it is possible to select 2n lattice points with x,y in [1,n] such that no three are in a straight line (where "straight line" means any line in the plane--not ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

Given an open subset U in n-dimensional space and two compact subsets C_0 and C_1 of U, where C_1 is derived from C_0 by a continuous motion, is it possible to move C_0 to ...

Given two crossed ladders resting against two buildings, what is the distance between the buildings? Let the height at which they cross be h and the lengths of the ladders ...

A (Delta,D)-graph is a graph with maximum vertex degree Delta and diameter at most D. The order of a graph with degree Delta of diameter D is bounded by ...