Hackenbush On a Number Line [Part 1]

Check out this video to see how to play Hackenbush:

If you want to play this game, I suggest having one person draw any starting position they’d like. The other player chooses colors and goes first.

I find this game to be much more fun to analyze than it is to play–there seems to be a curious connection between familiar numbers and Hackenbush positions.

I’ll leave the ball in your court.

Zero Game half+half+(-1)
bluered+bluered+red makes a zero game.
  1. Check that this game from the end of the video is actually a zero game.
  2. What number makes sense for this mystery position called bluered?
  3. Can you make sense of a position that is three pieces tall? Say blueredred?
  4. What other numbers can you find on the Hackenbush Number Line?

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