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My post from yesterday on permutation roots ends with a Mathematica code for finding the probability that a permutation of n elements has a kth root. This is done by finding the co...
C1 binomial expressions: fixed pairs, order, and meaning in context.
Combinatorial problems can be interesting for their own sake, but they are more interesting when there is a connection to a problem outside combinatorics, and the more unexpected t...
The previous post looked at the idea of storing a cryptographic key in the order of a deck of cards. A deck of 52 cards can store 225 bits of data because вЊЉlog2(52!)вЊ‹ = 225. He...
Not a true story, but inspired by this question. A while back, I found a probability problem with a rather striking answer. I still know the answer, but I can't seem to remember th...
Referencing this post : a partial challenge. An n x n board filled with numbers 1 to n is an aggregated nc coins solution if it for given n incrementally provides all c solutions f...
You (Alice) and your friend (Bob) have been captured by an evil squirrel. It will only release you both if you can win a game it proposes. You stay in the room. Bob leaves. The squ...
A few days ago I wrote a post on counting rooted trees. That post looked at the sequence c(n) which counts the number of rooted trees with n nodes. Here one node is distinguished a...
This is, oddly enough, a true story. Making a square out of squares. Many years ago, I was playing around with some semaphore flag squares (two triangles, one white, one coloured)...
We were attending one of my daughter’s friends’ birthday parties, where they had a game involving sitting in a circle. It’s kinda like musical chairs but every time a kid is out of...
The first post in the recent series of posts on Hadamard matrices describes a way of constructing new Hadamard matrices from two other Hadamard matrices by taking their Kronecker p...
Jason has some cards, each labelled with a distinct positive integer. Please prove to him that he can choose strictly more than half of the cards, so that there does not exist thre...
Forty-five students from nine different schools, five from each school, are been invited to take part in a cycle of a Mathematics Circle. During each of the planned sessions, the f...
Let σ be a permutation on n elements. If there is a permutation τ such that applying τ twice has the same effect on the list of elements as applying σ once, we say σ = τ² and τ is...
You have been invited to a rather unusual dice tournament. Before the tournament begins, every player is given a blank fair six-sided die and asked to write one non-negative intege...
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