Today you’re going to get the chance to prove a theorem no one has ever proved before.
First, the basic puzzle: What is the least number of straight lines you need to draw across a 3x3 square grid (illustrated left) so that every cell in the grid has at least one of the lines passing through it.
I’ve called this the Zorro puzzle since it makes me think of a swordsman slicing through every cell in the grid in the most efficient way possible.
Also, it came to me via Spain.
Carlos D’Andrea, at the University of Barcelona, told me that most of his brightest students get the wrong answer.
Which leads on to the next puzzle:
What is the least number of straight lines you need to draw across a 4x4 square grid (illustrated left) so that every cell in the grid has at least one of the lines passing through it.
The answer is probably less than your gut response.
Now for the serious bit. Is there a solution to the general problem:
What is the least number of lines you need to draw across a n x n square grid so that every cell in the grid has at least one of the lines passing through it.
Neither Carlos nor I (nor anyone else, to our knowledge) have looked at grids larger than 4x4. Maybe some of you could look at 5x5, 6x6 to see if a pattern is emerging?
I’ll be back at 5pm UK with the answers to the first two puzzles, and some discussion about the general case. If you want to tweet me your solutions please do at @alexbellos.
UPDATE: The solutions are now posted here
I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.
I’m the author of Football School, a book series for 7 to 12 year olds that opens up the curriculum through football. Football School Star Players: 50 Inspiring Stories of True Football Heroes is just out. It profiles 50 footballers who show that football can be a force for good both on and off the pitch.
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