The Black Hole

I seem to have been using quite a few games involving counting this term, and I find there are half a dozen of them in my repertoire.  Some of them you’ll know, but I’m pretty sure there are some you won’t, so it seemed like quite a good idea to put them up here.


You won’t have come across this one unless you’re familiar with the website of William Gibbs.  He calls it The Chief, but I think The Black Hole fits perfectly.  I’ll say more about William later, but first, here’s his game.


Any number can play; if there are only a few of you then you may wish to allow each player three lives.  You need about a dozen counters, and one should be different from the others.  Lay them out in a circle; I’m using bottle tops, and the purple one is The Black Hole. Black Hole (0) You also need to choose a “counting number”.  The counting number is the same for each player; I’m going to use 3. The first player chooses one of the green counters to start from, and counts “1”. Black Hole (1) She continues to the next counter: “2”. Black Hole (2) And the next: “3”. Black Hole (3) 3 is the counting number, so her turn ends and this counter is removed: Black Hole (4) The next player restarts the count with the next counter: “1” Black Hole (5) Then “2”: Black Hole (6) And “3”: Black Hole (7) Counter 3 is removed: Black Hole (8) And the next player begins the count again, starting with the next counter. “1”: Black Hole (9) “2”: Black Hole (10) “3” – Oh, dear, she lands in The Black Hole, and loses a life. Black Hole (11) .

Note that The Black Hole is NOT removed, and the next player begins counting at the counter after the Black Hole: Black Hole (12) Play continues until only one player survives (or until all the green counters have been used up).


I don’t know if anyone has analysed this game, because there’s a lot to explore – different numbers of counters, and different counting numbers, for a start. William’s own website makes a couple of observations about what happens in the simplest of situations, but says the analysis “becomes complex” – and that’s with just a handful of counters!

He also suggests there’s nothing to stop you playing with two Black Holes!

I first made contact with William Gibbs when I was going out to do some work with teachers in disadvantaged schools in South Africa.  I knew William had produced a lot of ideas using only the very simplest of materials – lengths of string, used matches, shells, ….

You can find an absolute cornucopia of ideas at his website:    From the home page, click on Pebble Puzzles and you can go to The Black Hole (William’s “The Chief”).




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