Sylver Coinage News

2008-01-25

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 4n+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.


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