Saturday, 27 April 2013

Hailstone Numbers

Friday morning I put on my cycle helmet and pedalled down to the library for the weekly Coffee Morning. This is happening every Friday 10.30-12 – in the hopes it will bring more people into our fine establishment, to borrow books/use the computers/etc./etc.


There’s usually a good crowd and we enjoy a great chat along with the drinks and biscuits. I had to delay my homeward journey though, due to a sudden, heavy hailstorm. When I got outside, Hannah-the-Bicycle had loads of hailstones in the basket! [note to self, next time, take a plastic bag to put over the saddle to keep it dry!]


Do you know about hailstone numbers?

You make a sequence like this – pick a number, if it is even, halve it, if odd then multiply by 3 and add 1. Examples

1  4  2  1  4  2  1  4  2  1…

3  10  5  16  8  4  2  1  4  2  1…

7  22  11  34  17  52  26  13  40  20  10  5  16  8  4  2  1  4  2  1…

15  46  23  70  35  106  53  160  80  40  20  10  5  16  8  4  2  1…

What is weird is that it appears that whatever number you start with, you end up with the repeated 4  2  1 sequence. The “Collatz Conjecture” says it will always be true, whatever ‘seed’ you start with, but it’s unproven, I believe. The ‘hailstone’ name comes from the fact that the numbers display multiple descents and ascents like hailstones in a cloud. [see here for more info]

I confess that I find it easy to waste hours playing with numbers seeing how quickly I get to the 4 2 1 pattern.


  1. We learnt this week that for The Test Mattman needs to be able to do triangle, square and cube number sequences. One of many, many times when I could write, "Wish you were here!"

  2. Use a lego base board and count the dots for square sequences.
    And build up bricks [the little 4x4 ones] in flat pyramid shapes to help count out triangle numbers.
    Your house is FULL of Lego, and it is a great counting resource


  3. I wish you had been my Maths teacher. You'd have to be a lot older but, all the same...
    Jane x

  4. How fascinating - I must try that for myself! Jx

  5. I've never come across this one before and I've had a good old mosey round t'internet reading up about the hailstone numbers. Thanks for planting the 'seed'.
    Love from Mum


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