Optimization chooses the best feasible row, not just any feasible row. This is CP-SAT-style exhaustive search on tiny data; real solvers use propagation and clause learning.
Search and Optimization
Example
Optimization chooses the best feasible row, not just any feasible row. This is an exhaustive-search view on tiny data; unlike a real CP-SAT solver, it does not propagate constraints or learn clauses.
highlighted = computed this step
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 \begin{array}{c|c}\text{x=0 y=3}&\hlmath{\text{value=3x+2y=6}}\end{array} x=0 y=3 value=3x+2y=6
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\hlmath{\text{value=3x+2y=5}}\end{array} x=0 y=3 x=1 y=1 value=3x+2y=6 value=3x+2y=5
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\hlmath{\text{value=3x+2y=7}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\hlmath{\text{value=3x+2y=9}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\hlmath{\text{value=3x+2y=6}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 x=2 y=1 value=3x+2y=8 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\hlmath{\text{value=3x+2y=8}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 x=2 y=1 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6 value=3x+2y=8
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 x=2 y=1 value=3x+2y=8 x=2 y=2 value=3x+2y=10 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\hlmath{\text{value=3x+2y=10}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 x=2 y=1 x=2 y=2 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6 value=3x+2y=8 value=3x+2y=10
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 x=2 y=1 value=3x+2y=8 x=2 y=2 value=3x+2y=10 x=3 y=0 value=3x+2y=9 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\hlmath{\text{value=3x+2y=9}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 x=2 y=1 x=2 y=2 x=3 y=0 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6 value=3x+2y=8 value=3x+2y=10 value=3x+2y=9
Build the concrete table
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 x=2 y=1 value=3x+2y=8 x=2 y=2 value=3x+2y=10 x=3 y=0 value=3x+2y=9 x=3 y=1 value=3x+2y=11 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\text{value=3x+2y=9}\\\text{x=3 y=1}&\hlmath{\text{value=3x+2y=11}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 x=2 y=1 x=2 y=2 x=3 y=0 x=3 y=1 value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6 value=3x+2y=8 value=3x+2y=10 value=3x+2y=9 value=3x+2y=11
Read the table verdict
Compute the highlighted logic-table value.
x=0 y=3 value=3x+2y=6 x=1 y=1 value=3x+2y=5 x=1 y=2 value=3x+2y=7 x=1 y=3 value=3x+2y=9 x=2 y=0 value=3x+2y=6 x=2 y=1 value=3x+2y=8 x=2 y=2 value=3x+2y=10 x=3 y=0 value=3x+2y=9 x=3 y=1 value=3x+2y=11 verdict best x=3 y=1 value=11 \begin{array}{c|c}\text{x=0 y=3}&\text{value=3x+2y=6}\\\text{x=1 y=1}&\text{value=3x+2y=5}\\\text{x=1 y=2}&\text{value=3x+2y=7}\\\text{x=1 y=3}&\text{value=3x+2y=9}\\\text{x=2 y=0}&\text{value=3x+2y=6}\\\text{x=2 y=1}&\text{value=3x+2y=8}\\\text{x=2 y=2}&\text{value=3x+2y=10}\\\text{x=3 y=0}&\text{value=3x+2y=9}\\\text{x=3 y=1}&\text{value=3x+2y=11}\\\text{verdict}&\hlmath{\text{best x=3 y=1 value=11}}\end{array} x=0 y=3 x=1 y=1 x=1 y=2 x=1 y=3 x=2 y=0 x=2 y=1 x=2 y=2 x=3 y=0 x=3 y=1 verdict value=3x+2y=6 value=3x+2y=5 value=3x+2y=7 value=3x+2y=9 value=3x+2y=6 value=3x+2y=8 value=3x+2y=10 value=3x+2y=9 value=3x+2y=11 best x=3 y=1 value=11
logic-computation
Every row is intentionally ordered and pinned to the lesson specification.