With the completion of the ECW infantry, I was once again
encouraged to look at the rate of increase in my collection of painting
bottle-tops, and also the likely trend in the sizes of my future
figure-painting batches. The two curves do not meet, my friends. I have reached
a situation where I cannot throw out a bottle-top of the two proscribed types
(Tesco’s fizzy mineral water for infantry and Tesco’s semi-skimmed milk
containers for cavalry); the collection is continuing to grow without purpose,
simply because it has been doing so for a while and it is hard to break a
habit.
So I have decided to keep 40 of the little ones and 30 of
the big ones, and throw the rest out. Sorry -
that should read “put the rest in the recycling bin”.
My son (who is 10) is a real maths enthusiast, so we spent a
little while piling them up before they went away, and did some messing around
with tetrahedral pyramids, and a touch of gentle finite difference theory to
see if we could construct a formula for the number of bottletops in a
tetrahedron of side n (and so on). Oh
what fun....
We had enough of the smaller tops to make a tetrahedron with
a side of 11 tops, it turns out, which our formula tells us contains 286
bottletops. It did occur to me that if I have the spare time to fiddle around
with this stuff (it was for the boy, really...) then someone else might have
the time to look at a photograph of the event.
![]() |
| The eleventh tetrahedral number is 286 |
Good, eh?
We have subsequently thrown them out (though it was a
struggle to part with them in the end), together with the other surplus tops
which didn’t fit into the construction. Now then, at 500ml a bottle, let’s
ponder how much water that represents, and where it has all gone now. And then
there’s the gas...
Hmmm.























