There Are Polar Bears Round The Icehole

It’s good to know that something you’ve done has stuck with someone; out of the blue I had a call from someone I hadn’t seen for ten years or more.  “Hello Alan, can you remind me about the Polar Bears?”

So here’s the activity that Gaynor wanted to talk about.

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I roll five dice: POLAR 13456

“There are six polar bears round the ice-hole.”

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Again:POLAR 23446

“There are two polar bears round the ice-hole.”

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Once more:POLAR 12226

“There are no polar bears round the ice-hole.”

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It’s much the best fun to do this informally when you can test out all sorts of ideas, but I’ll have to tell you that the colours of the dice don’t matter, nor their size, nor their positions.  (Generally speaking, I’ll use five dice, but we could use a different number.)  We’re left with just one factor to consider, that it’s the numbers showing on the top faces of the dice.

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Here are a few more:POLAR 12334

“There are four polar bears round the ice-hole.”

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POLAR 14446“There are no polar bears round the ice-hole.”

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POLAR 23345“There are eight polar bears round the ice-hole.”

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POLAR 13556

“There are ten polar bears round the ice-hole.”

Any ideas?

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It begins to look as if the odd numbers are more importantly related to the number of polar bears than even numbers.  A bit of a surprise, perhaps, because you were probably tempted to think that six might be heavily involved – let’s check that out:POLAR 66666

“There are no polar bears round the ice-hole.”

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You’ll probably want to test this out further:POLAR 22466

“There are no polar bears round the ice-hole.”

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POLAR 13355“There are twelve polar bears round the ice-hole.”

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Both these seem pretty helpful.  It seems even numbers don’t contribute at all, but that it’s the odd numbers – particularly the higher ones – which build the score.

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 It’s sensible to try:POLAR 33333

“There are ten polar bears round the ice-hole.”

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And:POLAR 55555

“There are twenty polar bears round the ice-hole.”

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Also:POLAR 11111

“There are no polar bears round the ice-hole.”

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Well, you should be pretty well there now.

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It looks as if only the three and five dice are involved.  Actually, it was a bit misleading to tell you it’s the numbers showing on the dice, because in fact it’s the patterns of the dots.

.It’s polar bears round the ice hole, remember?  And only three dice patterns have a central dot to show the ice hole – the one, the three and the five.  So on the three there’s a central hole with two bears around it, and the five has a hole with four bears round it (and though the one shows the ice hole, there are no bears around it!).

Now, all this is great fun with a group of children and adults as well, but that doesn’t mean it’s trivial.  Think of all the work you have to do.  You’ll be involved in hypothesising and testing, assessing your results, refining and improving your ideas.  Games like this give you a quite excellent insight into the process of scientific thinking and exploration – and I warn you I’ve a whole hatful of them.

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6 responses

  1. I love this idea. Just the thing to keep them guessing and trying different ideas.

    1. It’s pretty good fun when you’re down the pub as well!

  2. This was fun. It will get everyone in the classroom thinking, I’m sure.

    There is no ice-hole for the even dot patterns so sometimes it might be more correct to say, ” There are no polar bears round an ice-hole.” What do you think?

    1. Fine. Everyone, myself included, should always interpret and adapt ideas to suit their own style. You’ve made me think that it might be a good idea to say “round an ice-hole” / “round ice-holes” as appropriate.

  3. Reblogged this on Find the Factors and commented:
    This is a fun puzzle to try on kids or adults. How many polar bears are around an ice-fishing hole? Get out your Yahtzee dice and see who can figure out the pattern of the riddle.

  4. I’ve usually seen this game referred to as “petals around the rose.”

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