What is the maximum number of points that can be placed in a square of area $2$ units squared such that no two points are closer to each other than 2/3 units?
Initally, this seemed to me like a problem for the pigeonhole principle, however I gave up on that idea and just used common sense. I drew the following picture:
This shows you can fit 9 points which are all 2/3 units away from each other, however, the maximum is apparently 8. I feel I have made a simple mistake, could anyone help?
Many thanks.