In the Fountain Cafe in Ingleton there is a game of solitare, consisting of a triangle of pegs, with a base of five. Some (ex)members of CUCC decided to cheat a little bit, and work out the solutions with the aid of a Computer. The first attempt was in Fortran by AERW, on the IBM 370/165 as he thought that it would be more likely that a few pages of games would be overlooked in a teaching establishment than at his work. However, time was against him.
The challenge was taken up by ADWG, who with the aid of a one share project, the PL/I checkout compiler and a refusal to work antisocial hours, was soon forbidden from using the machine at any time. A twenty second run managed to make eleven MOVES! He had deduced that there were less than forty possible solutions, and was to be found grovelling for a few minutes of CPU from anyone with computer access. I decided to jump to his assistance, and wrote a little program, and set it running on one of the research computers. To my suprise the program aborted having run out of disc (it only had 180Mb). I therefore removed the statements to print the moves, simply counting the solutions as I found them.
The results were (final peg: number of solutions)
|Peg A||A:3408||G: 720||J:2688||M:8064|
|Peg B||A:3408||G: 720||J:2688||M:8064|
|Peg D||C:4907||D:25726||I: 775||L:3157||O:8064|
|Peg E||M: 775|
All these results must be multiplied by six for all symetric solutions, giving a total of 438,984! The 'Clever' solutions, those ending on the starting square, are Peg A (3408) and Peg D (25726).
The original idea was to print the solutions, but it would take 6754 pages - a bit beyond the scope of this publication! However, here are a few. abc means move peg a over peg b into c and remove peg b.
dba fed acf gdb jfc mhd bdg kgd onm lmn nie def fca
dba fed acf gdb jfc mhd bdg onm kgd lmn nie def fca
dba fed acf gdb jfc mhd bdg onm lmn kgd nie def fca
dba fed acf gdb jfc mhd bdg onm lmn nie kgd def fca
dba fed acf gdb jfc mhd onm bdg kgd lmn nie def fca
dba fed acf gdb jfc mhd onm bdg lmn kgd nie def fca
dba fed acf gdb jfc mhd onm bdg lmn nie kgd def fca
dba fed acf gdb jfc mhd onm lmn bdg kgd nie def fca
dba fed acf gdb jfc mhd onm lmn bdg nie kgd def fca
dba fed acf gdb jfc mhd onm lmn nie bdg kgd def fca
dba fed acf gdb jfc lhe nml klm mif cfj ojf fed dba
dba fed acf gdb jfc nie lmn onm mhd bdg kgd def fca
(more on application)