Sylver Coinage
Definition
Sylver Coinage is a mathematical
game invented by John Horton Conway.
Two players take turns choosing numbers, which represent denominations
of money.
A player may not name a number that can be expressed as a sum
(with multiples) of some previously chosen numbers.
The player who names 1 loses.
News of Sylver Coinage
Statement of the Progression Hypothesis
Care and Feeding of Enders
A Glossary of Sylver Coinage
Richard K. Guy's Twenty Questions
Tables
- Some Very Long Positions
- Winning Moves in {m,n} Positions
- Some 𝓟-Positions With g>1
- Responses to Moves in {14,26}
- Responses to Moves
in {16,22,24,26,28,30,34}
- Responses to Moves in {18,30,32}
- Winning Odd Moves in Even 6-Positions
- Winning Moves in Positions with
Numbers 6–14
Refereed Papers
Reports
- New Results In Sylver Coinage (1991)
[ GNUzipped DVI |
PostScript ]
Summary of previous work, many new computational results,
proof of the Single Win Theorem, and a short bibliography.
-
Late News of Sylver Coinage (1996)
[ GNUzipped DVI
| PostScript
]
Some advanced computational results, including the solution of
{8,30,34} and a new long even position with no odd winning move.
-
Sylver Coinage positions with g=2 (2021), by Thomas Blok.
Full analysis of all even positions containing an even number from 2 to 10.
[ Microsoft Word
| Adobe Portable
Document Format (PDF)
]
-
Sylver Coinage even positions in 14 (2022), by Thomas Blok.
Full analysis of all even positions containing the number 14.
[ Adobe Portable
Document Format (PDF)
]
Software
My production software is not yet available.
Meanwhile, here is a simple Perl script
for computing winning moves in Sylver Coinage positions.
Col. George Sicherman
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