CTK Insights

Archive for the 'Combinatorics' Category

26 Apr

Not too easy - not too difficult

TweetThe other day, while driving my HS senior son to school (he could have taken a bus, but, for one, his time is at a premium; also, the drive gives us an opportunity for a small chat), we talked about how words with different basic meanings may mean the same thing in certain contexts. As […]

01 Apr

Doodling on April 1st

TweetI came across the following problem several days ago but hesitated to write about it until April 1st. It is simple, practically trivial, and still, after doodling with it for some time, I was left with an open question. If it appears too trivial, even unworthy of mention, do please make an allowance for the […]

20 May

Probabilities in a Painted Cube

Now generalize: cut the cube into nxnxn smaller cubes and ask the same question. The problem is not awfully difficult but needs some figuring out. Following the foregoing pattern, we eventually arrive at 1/n. But here is a delightful shortcut

05 Jul

A Funny Lapse in a Wonderful Book

In order for the last sentence to follow the suggested convention it had to be written as "If there are no rectangles in the tiling ...". To accept the sentence as is, the convention had to be "From this point on, we shall refer to a rectangular tile as simply a rectangle." I hope I am not being disgustingly pedantic, but some times this does happen.

25 Dec

In Pursuit of the Traveling Salesman

Tweet It's a rare pleasure to get a good book ahead of its planned publishing date. In Pursuit of the Traveling Salesman by William Cook that was expected at the beginning of 2012, was delivered yesterday right to my door. My first impression is that this is the sort of a book that are read […]

21 Dec

Star of David Theorems in Pascal Triangle

TweetI am not sure who coined the term "The Star of David Theorem" to designate the identities discovered in the early 1970s. There are in fact two of them, both related to the "Star of David" configuration in Pascal triangle (The diagram is courtesy wikipedia.org.) The first result discovered by Hoggatt and Hansell in 1971 […]

24 Oct

Combinatorial Mathematics with Applications: an Example

TweetIn their textbook Discrete Algorithmic Mathematics authors Stephen Maurer and Anthony Ralston offer a light-hearted example [pp. 217-221]: When checking into a hotel nowadays, sometimes a guest receives a four-digit "combination", not a key. On the door of each room is a keypad. Any time those four digits are entered in the proper sequence (regardless […]

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