998001

This is one of my favourite maths “tricks”.

If you work out 1/998001 as a decimal then you get list of all (well very nearly all) the 3-digit numbers. To be specific:

1/998001 = 0.000 001 002 003 004 005 006 007 008 009 010 011 012 … 123 124 125 … 246 247 248 … 789 790 791 … all the way up to 990 991 992 993 944 995 996 997 999 …

So that’s a list of all the 3-digit numbers, but 998 is missing! Then the sequence repeats, for ever.

This is maths, so it’s not actual magic and there is an explanation. That said, even though I’ve seen a lot of these sorts of tricks and puzzles, when I first saw it it certainly looked like a lot like magic to me.

(Explanation to follow, though maybe you can work it out yourself.)