Home Math Games Entrapment

Rearrange the gray circles so each red circle lies on the midpoint of a segment connecting two gray circles.

Note: If you would like to have the site keep track of your progress through these puzzles instead of presenting them to randomly, please Login.

Game Instructions

In this game, your job is to rearrange a set of gray circles in a square playing field, in such a way that the red circles (already on the playing field) all lie exactly halfway between two gray dots. Another way of saying this, every red dot must be the midpoint of a line segment connecting two gray dots on the playing field.

The following image is a simple 'Entrapment' puzzle. There are four red dots, and four gray dots.

In solving this puzzle, the first thing I notice is that one of the red dots is against a "wall". The only way to trap this dot is by placing two of my gray dots somewhere along that same wall, on either side of the red dot, and equidistant from it. I decide to try putting my dots directly adjacent to it:

In studying the game board, I realize I can place my next dot in such a way that it traps two of the computer's dots simultaneously:

We're almost finished; we have one more dot to place, and that one dot must trap the computer's remaining red dot. Can you do it? Can you find two ways to place the remaining dot?

Puzzle Hint

Start out by trying some of the "Practice" puzzles. These are all puzzles which contain exactly three red and three gray dots. What you will discover is that most puzzle solutions are built around triangles, so if you can master the easy puzzles, the more challenging puzzles can be broken down into smaller, more manageable pieces. The following blog entry explains a little bit more about the geometry of this puzzle: The Geometry Of Entrapment