36,594 research outputs found
Diagonal Peg Solitaire
We study the classical game of peg solitaire when diagonal jumps are allowed.
We prove that on many boards, one can begin from a full board with one peg
missing, and finish with one peg anywhere on the board. We then consider the
problem of finding solutions that minimize the number of moves (where a move is
one or more jumps by the same peg), and find the shortest solution to the
"central game", which begins and ends at the center. In some cases we can prove
analytically that our solutions are the shortest possible, in other cases we
apply A* or bidirectional search heuristics.Comment: 20 pages, 11 figure
Solving Triangular Peg Solitaire
We consider the one-person game of peg solitaire on a triangular board of
arbitrary size. The basic game begins from a full board with one peg missing
and finishes with one peg at a specified board location. We develop necessary
and sufficient conditions for this game to be solvable. For all solvable
problems, we give an explicit solution algorithm. On the 15-hole board, we
compare three simple solution strategies. We then consider the problem of
finding solutions that minimize the number of moves (where a move is one or
more consecutive jumps by the same peg), and find the shortest solution to the
basic game on all triangular boards with up to 55 holes (10 holes on a side).Comment: 23 pages, 14 figures; published version including comments by John
Beasle
Fringe field simulations of a non-scaling FFAG accelerator
Fixed-field Alternating Gradient (FFAG) accelerators offer the potential of
high-quality, moderate energy ion beams at low cost. Modeling of these
structures is challenging with conventional beam tracking codes because of the
large radial excursions of the beam and the significance of fringe field
effects. Numerous tune resonances are crossed during the acceleration, which
would lead to beam instability and loss in a storage ring. In a non-scaling
FFAG, the hope is that these resonances can be crossed sufficiently rapidly to
prevent beam loss. Simulations are required to see if this is indeed the case.
Here we simulate a non-scaling FFAG which accelerates protons from 31 to 250
MeV. We assume only that the bending magnets have mid-plane symmetry, with
specified vertical bending field in the mid-plane (y=0). The magnetic field can
be obtained everywhere using a power series expansion, and we develop
mathematical tools for calculating this expansion to arbitrary order when the
longitudinal field profile is given by an Enge function. We compare the use of
a conventional hard-edge fringe with a more accurate, soft-edge fringe field
model. The tune 1/3 resonance is the strongest, and crossing it in the
hard-edge fringe model results in a 21% loss of the beam. Using the soft-edge
fringe model the beam loss is less than 6%.Comment: 12 pages; 12 figure
Enthusing and inspiring with reusable kinaesthetic activities
We describe the experiences of three University projects that use a style of physical, non-computer based activity to enthuse and teach school students computer science concepts. We show that this kind of activity is effective as an outreach and teaching resource even when reused across different age/ability ranges, in lecture and workshop formats and for delivery by different people. We introduce the concept of a Reusable Outreach Object (ROO) that extends Reusable Learning Objects. and argue for a community effort in developing a repository of such objects
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