## Wild four digit quaternaries

Solutions to wild quaternary games PDF (Aaron Siegel).Aaron has also found a solution for the wild octal game **0.144**.

More information here (background paper) and here (my original problem statement, presented at the Banff CGT conference problem session last month).

More tidbits from Aaron:

0.01222 has period 8 and quotient order 370

0.10322 has period 8 and quotient order 214

## Solution to Guiles

Aaron Siegel has found a complete analysis of the misere play of Guiles (Guy and Smith octal code 0.15) by using his recently developed standalone java program, *MisereSolver*.

The misere quotient semigroup of Guiles has 42 elements, and its pretending function has period 10.

There will be a paper coming out in the next year or so that gives more information. If you want to wade through the details now, before it’s cleaned up for publication, here’s the solution file that gives its misere indistinguishability quotient semigroups to heap 160. That’s more than long enough to guarantee that the periodicity continues indefinitely. And here’s an even bigger log file documenting the same computation, also to heap 160.

## MisereSolver

Aaron Siegel has already whipped together an amazing Java program for everything in my misere CGT paper, while also incorporating his own insights into algorithms for misere quotient semigroup computation. Given an octal game code as input, his program directly computes a presentation of its misere quotient semigroup to heap size n=1, 2, 3, in turn, together with the associated pretending functions and outcome partitions at each heap size n. He’s solved .15 (Guiles), .115, .114, and a bunch of wild quaternary games using this software.

Eventually his software will make into cgsuite, I hope.

## Taming the Wild in Impartial Combinatorial Games

My paper “Taming the Wild in Impartial Games” has been accepted by INTEGERS. Aaron Siegel and Dan Hoey helped me by pointing out some mistakes in section 11.5 that I’ve corrected in this new and (hopefully) final version that I just put into the arXiv.

## Seventeen quaternary bounties claimed

Aaron Siegel has claimed 17 of the 21 quaternary bounties. Still open are .3102, .3122, .3123, and .3312. That’s $425 in bounties for Aaron, but there’s still $100 on the table…