Problem 6

To celebrate the turn of the year, Light R Us designed a prototype for a large light feature, consisting of 2025 lightbulbs arranged in a 45-by-45 grid. There is also a button in each position which switches all the lightbulbs in its row and column at the same time. Pressing the button turns on any lightbulbs which were off, and turns off any lightbulbs which were on.

The prototype was a success among factory workers who enjoyed creating different patterns of light. Starting with all bulbs off and pressing some buttons, what is the largest possible number of lightbulbs that can be on at a given time, if at least one lightbulb is off?

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is five plus seven, subtract six?

This problem was first solved on Wed 26th February at 4:02:37pm