You have a four-by-four array of padlocks, interconnected by the following mechanism: every time you use a key to lock/unlock one of the padlocks, all of the other padlocks in its row and column switch from locked to unlocked and vice versa. Determine whether it's possible to unlock all of the boxes no matter the starting configuration.

Click on a padlock to switch between locked and unlocked position (without affecting the locks in its row and column). Shift-click to toggle all the locks in a row and column Unlocking solution: proposed solution for unlocking the configuration shown on the left. Hold spacebar view solution.