Related papers: Three problems for the clairvoyant demon
Run-and-tumble particles confined between two walls seem like a simple enough problem to possess analytical tractability. Yet up to date, no satisfactory analysis is available for dimensions higher than one. This work contributes to the…
The constrained Dirichlet boundary value problem $\ddot x=f(t,x)$, $x(0)=x(T)$, is studied in billiard spaces, where impacts occur in boundary points. Therefore we develop the research on impulsive Dirichlet problems with state-dependent…
Most theoretical definitions about the complexity of manipulating elections focus on the decision problem of recognizing which instances can be successfully manipulated, rather than the search problem of finding the successful manipulative…
We investigate some versions of the famous 100 prisoner problem for the infinite case, where there are infinitely many prisoners and infinitely many boxes with labels. In this case, many questions can be asked about the admissible steps of…
The Frobenius coin problem in three variables, for three positive relatively prime integers $a_1< a_2< a_3$ asks to find the largest number not representable as $a_1x_1+a_2x_2+a_3x_3$ with non-negative integer coefficients $x_1$, $x_2$ and…
A variant of the classical knapsack problem is considered in which each item is associated with an integer weight and a qualitative level. We define a dominance relation over the feasible subsets of the given item set and show that this…
Given a dollar, how many ways are there to make change using pennies, nickels, dimes, and quarters? What if you are given a different amount of money? What if you use different coin denominations? This is a well known problem and formulas…
Motivated by a problem on the 67th William Lowell Putnam Mathematical Competition, we will summarize three different solutions found on a website. This Putman problem is a special case of Sylvester's four point problem! Suppose four points…
We show that the phenomenon of anomalous weak values is not limited to quantum theory. In particular, we show that the same features occur in a simple model of a coin subject to a form of classical backaction with pre- and post-selection.…
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
In this paper we first study the isoperimetric problem in the case of integer triangles, as well as Alcuin's sequence and how it relates to the number of different integer triangles with a given perimeter. We then present and compare two…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the…
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio of circles, but some configurations have fewer than eight…
A cosmological theory that predicts a late-time accelerated attractor with a constant dark matter to dark energy ratio can be said to solve the Coincidence Problem. Such cosmologies are naturally generated in the context of non-standard…
We formally investigate some computational obstacles to tractability of computing the variety determined by K complex polynomials in N boolean variables. We show that using algebraic methods for solving combinatorial problems, the obstacles…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…
This chapter does not deal with specific tools and techniques for managing complex systems, but proposes some basic concepts that help us to think and speak about complexity. We review classical thinking and its intrinsic drawbacks when…
The present paper formulates and solves a problem of dividing coins. The basic form of the problem seeks the set of the possible ways of dividing coins of face values 1,2,4,8,... between three people. We show that this set possesses a…
We deal with some of problems posed by Monk and related to cardinal invariant of ultraproducts of Boolean algebras. We also introduce and investigate some new cardinal invariants.