GF(2) / RANK / CHECKED HINTS
Every lamp.
One exact equation.
Press a switch to XOR its column into the lamps. Edit the matrix or flip a lamp directly to explore consistency, freedom and contradictions.
Lights and switches
Ruler reach is 2^v₂(column+1) horizontally and 2^v₂(row+1) vertically, with the pressed cell included. The preview boards are 3 × 3.
Minimum means fewest additional switches from the current state. All 2ⁿ assignments are checked, with n ≤12 and at most 24 equations. The smallest integer bitmask breaks minimum ties. Free columns are independent parameters; other dependent variables need not be forced.
Switch-to-lamp matrix
Rows are lamps. Columns are switches; click a coefficient to change one connection.