One thing that is worth
presenting publicly is one of the car we designed, that was not been
solved by any other participant. Producing as many such cars as
possible was indeed a key to reach a high score in this contest, but unfortunately
we started to submit such these cars only 5 hours before the end. Here is one such car, numbered 159028,
displayed in ASCII art using one of our programs.
15 chambers, 4 tanks
/-0--1-
M
\-1-
/-1--0-
A
\-1^2--0-
/-1--2-
A
\-1^2--2-
/-1--3-
A
\-1^2--3-
/-2--1-
M
\-1-
/-3--1-
M
\-1-
/-1^2--0-
A
\-1--0-
/-1^2--2-
A
\-1--2-
/-1^2--3-
A
\-1--3-
/-0--1--2--3-
A
\-0--1--2--3-
/-1--0--2--3-
A
\-1--0--2--3-
/-2--0^2--2--0^3--3--0--3--0^2--3-
A
\-3^12--2--3^2--2--3^9--2--3^7--0--3^15--2--3^2--2--3^13--2--3^9--2--3^18--2--3^28--2--3^52--2--3^3--2--3^6--2--3^8--2--3^18-
/-0--3^6--0^5--3^3--0--3--2--3--0^6--3--0^2--3--0^3--3--0^2-
A
\-2^2--3--2^154--0--2^45-
/-2^2--3--2^154--0--2^45-
A
\-0--3^6--0^5--3^3--0--3--2--3--0^6--3--0^2--3--0^3--3--0^2-
/-3^12--2--3^2--2--3^9--2--3^7--0--3^15--2--3^2--2--3^13--2--3^9--2--3^18--2--3^28--2--3^52--2--3^3--2--3^6--2--3^8--2--3^18-
A
\-2--0^2--2--0^3--3--0--3--0^2--3-
A fuel solution is
( 1 39943 )
tank 0 = ( )
( 0 1 )
( 1 0 )
tank 1 = ( )
( 1 0 )
( 1 3872 )
tank 2 = ( )
( 0 1 )
( 1 1191 )
tank 3 = ( )
( 0 1 )
Such a difficult car/fuel pair has been generated by encoding into
matrices a system of linear Diophantine equations. 16 other cars like
this have been submitted, having solutions in dimension 2, with
coefficients up of the same order of magnitude. None of them were
solved.
18 other of our cars were unsolved by any participants, these were generated using an encoding of equations with very large powers, whose solutions are of dimension 1 but with values typically around 2^{1000}