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Showing posts from October, 2012

Solving IMO 1989 #6 using Probability and Expectation

Representing a Number as the Sum of Three Squares using a Probabilistic Shotgun

See this post on MathOverflowEfficient Computation of Integer Representation as Sum of Three Squares.

One example:

8888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888…

A new 9-square featuring former NBA player Ron Mercer

A new 9-square featuring former NBA player Ron Mercer:

aggressin gerontine grantinge ronmercer entercall stirchley sincaline ingelends neerlyest
Statistically, my estimate is that I need about 76419 words in my 9-letter word list to find a single 9-square. I have 223602, so the expected number is (223602/76419)^9 = 15270 total 9-letter word squares that can be found using this word list. We'll see how close my estimate comes.

The Mathematics of Square Construction