1xN
Optimal Domination Numbers
Solutions and Proofs
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D(1,N) = the domination number for a board with 1 row and N columns.
D(1,N) = N for N >= 1
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Sufficiency proof.
D(1,N) <= N.
Sufficiency is proved by showing a feasible solution
using the domination number of knights.
Such a feasible solution is produced by occupying all squares.
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Necessity proof.
D(1,N) >= N.
Knights cannot attack within the same row.
Since no square can be attacked,
all squares must be covered by occupying them.
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