On Aug 4, 2:59 pm, Offray Vladimir Luna Cárdenas
<[email protected]> wrote:
>
> Thanks also. Works on Firefox on an arch linux over intel centrino. This
> could be a project for an interested student.
>
You can get a solution with the following short Sage code:
def weight(v):
return sum([1 for i in v if i==1])
def solve_lights(n):
g = graphs.Grid2dGraph(n,n)
M = g.adjacency_matrix().base_extend(GF(2))
M = M+diagonal_matrix(GF(2),[1 for i in range(M.nrows())])
v = vector(GF(2),[1 for i in range(M.nrows())])
NS = M.kernel()
sol = M\v
print 'a solution:'
print matrix(n,list(sol))
print 'computing minimal solution'
min_w = weight(sol)
for i in NS:
new_sol = i + sol
new_weight = weight(new_sol)
if(new_weight < min_w):
sol = new_sol
min_w = new_weight
min_sol=matrix(n,list(sol))
return min_sol
The student can try to explain why this works :)
Or they can try to play the hexagonal version
http://www.math.uiuc.edu/~rkirov2/hexout/
Rado
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