Knight Stuffing II

Logic Level 2

If you place white and black knights on a 4 × 4 4\times4 chessboard such that every white knight is attacked by at least one black knight and every black knight is attacked by at least one white knight, what's the maximum number of knights possible?


The answer is 16.

View wiki
Jason Dyer by Jason Dyer

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Paul Hindess
Dec 16, 2016

We can, for example, place 8 of each colour in a checkerboard pattern by placing them on squares of their own colour. But there are many possible solutions that achieve this maximum.

Perhaps we could also ask:

  • How many different ways (counting rotations and reflections as identical) can a 4x4 board be filled with black and white knights such that every white knight and every black knight is being attacked?
  • How many of these do not contain 8 of each colour?
  • What is the largest ratio of black to white that can be achieved?
1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...