$N1 \\ A11 \quad A12 \quad B11 \quad B12 \\ A21 \quad A22 \quad B21 \quad B22 \\ A31 \quad A32 \quad B31 \quad B32 \\ .... \\ .... \\ AN11 \quad AN12 \quad BN11 \quad BN12 \\ \quad \\ \quad \\ N2 \\ A11 \quad A12 \quad B11 \quad B12 \\ A21 \quad A22 \quad B21 \quad B22 \\ A31 \quad A32 \quad B31 \quad B32 \\ .... \\ .... \\ AN21 \quad AN22 \quad BN21 \quad BN22$

$Solution \quad For \quad The \quad Data Set \quad \# \quad 1 \\ x \quad Lamps \quad is \quad needed \quad at \quad least.\quad Their \quad possible \quad locations \quad are: \\ V11 \quad V12 \\ .... \\ .... \\ Vx1 \quad Vx2 \\ \quad \\ Solution \quad For \quad The \quad Data Set \quad \# \quad 2 \\ y \quad Lamps \quad is \quad needed \quad at \quad least.\quad Their \quad possible \quad locations \quad are: \\ V11 \quad V12 \\ ... \\ Vy1 \quad Vy2$