Category Archives: Math

Where I describe all things related to math, combinatorics, pose problems

The Wire Identification Problem

The Wire Identification Problem: Try to label the wires on the right with labels corresponding to those on the left

A bunch of n wires have been labeled at one end with alphabetic codes A, B… The wire identification problem asks for an efficient procedure to mark the other end of the bunch with the corresponding labels. The wires run underground so you can’t track them individually and any wire is visibly indistinguishable from any other (except for the labeling). Continue reading

On Asymptotic Methods in Analysis: Prof. de Bruijn’s beautiful little book

For the past several days, I’ve been working my way through Prof. N.G. de Bruijn’s book Asymptotic Methods in Analysis; and I want to share some of the fun I’ve had reading it.

This post is not a review or anything (here’s an image of the back cover with some reviews). Below are just fragments of what I’ve read so far and found fascinating. Continue reading

Read wrote Wright… Graph Theorists playing with words

Frank Harary, Oberwolfach (1972)

I was going through the first chapter of the book Graphical Enumeration by Frank Harary and Edgar M. Palmer when I chanced upon this perplexing footnote:

Read wrote Wright that both Read [R2]1 and Wright [W3]2 were wrong. So Read and Wright wrote a joint erratum [RW1]3 to set things right. This may be wrong since Wright asserts that Wright wrote Read first.

Continue reading

  1. [R2] R.C. Read, The number of k-colored graphs on labelled nodes, Canad. J. Math. 12, 409–413 (1960).
  2. [W3] E.M. Wright, Counting coloured graphs, Canad. J. Math. 13, 683–693 (1961).
  3. [RW1] R.C. Read and E.M. Wright, Coloured graphs: A correction and extension, Canad. J. Math. 22, 594–596 (1970).

Analytically evaluating a limiting probability (June 2007 Ponder This)

In this post, I’ll describe my solution to June 2007’s Ponder This. I had felt that my solution was kind of nifty, and different from the one that was published. It had actually taken me several days to work the whole thing out.

Here’s part (2), the tougher part, of the problem: Values for a random variable are generated independently and uniformly over \left[0,1\right). By accumulating these values, your job is to reach a sum between n+x and n+1, where n is a positive integer, and 0\,\textless\,x\,\textless\,1. Continue reading