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The monkey and the coconuts is a mathematical puzzle in the field of Diophantine analysis that originated in a short story involving five sailors and a monkey on a desert island who divide up a pile of coconuts; the problem is to find the number of coconuts in the original pile (fractional coconuts not allowed).
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. [1] It is a part of the Stack Exchange Network, but distinct from math.stackexchange.com.
The friendship paradox is the phenomenon first observed by the sociologist Scott L. Feld in 1991 that on average, an individual's friends have more friends than that individual. [1] It can be explained as a form of sampling bias in which people with more friends are more likely to be in one's own friend group. In other words, one is less likely ...
A substitution is called a ground substitution if it maps all variables of its domain to ground, i.e. variable-free, terms. The substitution instance tσ of a ground substitution is a ground term if all of t ' s variables are in σ ' s domain, i.e. if vars(t) ⊆ dom(σ).
78 of the 156 possible friends-strangers graphs with 6 nodes. The other 78 can be obtained by reversing the red and blue colours of each graph. For each graph the red/blue nodes shows a sample triplet of mutual friends/strangers. The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory.
Because of this, often, the only simple effective way to deal with multiplication by expressions involving variables is to substitute each of the solutions obtained into the original equation and confirm that this yields a valid equation. After discarding solutions that yield an invalid equation, we will have the correct set of solutions.
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