We show in this post that an elegant continued fraction for 
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Posts Tagged 'Combinatorics'
Derangements and Continued Fractions for e
Published December 31, 2020 Occasional Leave a CommentTags: Combinatorics, Number Theory
Arrangements and Derangements
Published December 24, 2020 Irish Times Leave a CommentTags: Combinatorics, Number Theory
Six students entering an examination hall place their cell-phones in a box. After the exam, they each grab a phone at random as they rush out. What is the likelihood that none of them gets their own phone? The surprising answer — about 37% whatever the number of students — emerges from the theory of derangements.
Order in the midst of Chaos
Published April 30, 2020 Occasional 1 CommentTags: Combinatorics, Graph Theory
We open with a simple mathematical puzzle that is easily solved using only elementary reasoning. Imagine a party where some guests are friends while others are unacquainted. Then the following is always true:
No matter how many guests there are at the party, there are
always two guests with the same number of friends present.
If you wish, try proving this before reading on. The proof is outlined at the end of this post.
Complete graphs with 6 to 10 vertices.
Folding Maps: A Simple but Unsolved Problem
Published February 14, 2019 Occasional Leave a CommentTags: Combinatorics
Paper-folding is a recurring theme in mathematics. The art of origami is much-loved by many who also enjoy recreational maths. One particular folding problem is remarkably easy to state, but the solution remains elusive:
Given a map with M × N panels, how many different ways can it be folded?
Each panel is considered to be distinct, so two foldings are equivalent only when they have the same vertical sequence of the L = M × N layers.
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