# God's Algorithm out to 18q*: 368,071,526,203,620,348

Submitted by rokicki on Sat, 07/19/2014 - 14:32.

Almost exactly four years after 17q* was announced by Thomas

Schuenemann, we have calculated the number of positions at a distance

of exactly 18 in the quarter-turn metric. This is more than one in

twenty positions.

This number matches (mod 48) the count of distance-18 symmetric

positions; this provides a bit of confirmation that it is correct

(or rather, about 5.6 bits of confirmation).

The approach we used does not permit us to calculate the number of

positions mod M or mod M+inv without significantly increasing the

amount of CPU required; these computations will have to wait for

someone with more ambition and more CPU time, or a different approach.

This new result is a part of our ongoing investigation into the

quarter-turn metric to complement the earlier work on the half-turn

metric. The bulk of the code is the same between this work and

that work, but some improvements have been made to search.

This work was supported in part by an allocation of computing time

from the Ohio Supercomputer Center.

Schuenemann, we have calculated the number of positions at a distance

of exactly 18 in the quarter-turn metric. This is more than one in

twenty positions.

This number matches (mod 48) the count of distance-18 symmetric

positions; this provides a bit of confirmation that it is correct

(or rather, about 5.6 bits of confirmation).

The approach we used does not permit us to calculate the number of

positions mod M or mod M+inv without significantly increasing the

amount of CPU required; these computations will have to wait for

someone with more ambition and more CPU time, or a different approach.

This new result is a part of our ongoing investigation into the

quarter-turn metric to complement the earlier work on the half-turn

metric. The bulk of the code is the same between this work and

that work, but some improvements have been made to search.

This work was supported in part by an allocation of computing time

from the Ohio Supercomputer Center.