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.

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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.

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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. 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”. She continues to the next counter: “2”. And the next: “3”. 3 is the counting number, so her turn ends and this counter is removed: The next player restarts the count with the next counter: “1” Then “2”: And “3”: Counter 3 is removed: And the next player begins the count again, starting with the next counter. “1”: “2”: “3” – Oh, dear, she lands in The Black Hole, and loses a life. .

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

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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: http://www.cyffredin.co.uk From the home page, click on Pebble Puzzles and you can go to The Black Hole (William’s “The Chief”).

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