The short position {18,24,34} is
**P**.

*2008-01-20*

The short position {12,32,62} is
**P**.

*2008-01-20*

The short position {12,32,58} is
**P**.

*2008-01-20*

The short position {12,32,54} is
**P**.

*2002-05-29*

The short position {12,28,58} is
**P**.
The lowest possible winning move in {12} with *g*=2
is 62.

*2002-04-29*

The long position {20,22,24,26,28,36} is
**P**.
At 797637 it enters a period of 230976.
Maybe long **P**-positions with *g*=2
are more common than I thought.

*2001-11-07*

The long position {16,22,24,26,28,30,34} is
**P**.
See this page for details.
It is rare for long positions to be **P**.

*2001-07-12*

The position {12,40,46} is
**P**.
Since {12,40,50} is already known to be **P**,
the lowest possible winning move in {12} with *g*=2 is 58.

*2001-05-04*

The position {18,30,32} is indeed
**P**.
For details see the list of responses.

*2001-02-28*

I have reorganized the Enders Page.

*2001-02-06*

The position {18,30,32} is probably
**P**.
I do not think I shall find a winning move in {18}.

*2001-01-13*

I had hoped to prove that {18,22} is **P**, but 79 wins.
Meanwhile I have found that 10 is the only winning move in {16,24}.

*2000-12-22*

The 6-position {6,50,94} has no odd winning move less than 10 to the 8th power. I may abandon this line of inquiry.

*2000-12-18*

I just added a new 6-position, and it's a whopper: {6,44,82} [4,5993171].

*2000-12-18*

I have added a table of winning odd moves in even 6-positions.

*2000-12-06*

I have added some new material to the Enders Page.

*2000-11-12*

I have started writing a page on enders.

*2000-08-25*

The position {16,26,88} is probably
P.
I had hoped that {16,26} would be **P**, because all other derived
short positions are **N**.

*2000-08-23*

I have posted a statement of the Progression Hypothesis, which characterizes the ender-status of positions whose moves are in arithmetic progression.

*2000-08-03*

The position {14,26} is P. For details see the list of responses.

*2000-07-29*

The position {14,26} is Probably P. Of course, even when such a big fish is hooked, it takes a lot of work to land it! This would give a complete first-order solution of {14}: [7, 8, 10, 26].

*2000-07-19*

The position {12,40,46} is **P**.
This means that the least possible winning move in {12} with
*g*=2 is 50.
Lower moves of the form 4*n*+2 are answered:
{10,12} [7,18]; {12,14} [16]; {12,18} [10,15,16,21];
{12,22} [16,30]; {12,26} [28]; {12,30} [22,...];
{12,34} [20,...]; {12,38} [20,...]; {12,42} [20,...]; {12,46} [40,...].

In fact, any given move in {12} with *g*=2 is likely to lose
because it has many replies that produce short positions.
If there exists a winning move with *g*=2, it is almost certainly
too high to compute.

Back to Sylver Coinage.

Col. G. L. Sicherman [ HOME | MAIL ]