On the recent Math Factor podcast episode GR, Cheim provided several puzzles from the book Riddles of the Sphinx by David J. Bodycombe. One the puzzles was to find the hidden logic in the sequence 0 1 8 10 19 and 90 and question why it couldn’t be continued.

But it can with the addition of 10^{24}.

If you want the answer to the sequence then read below. If not look away.

So to answer the puzzle you need to spell out the numbers,

zero one eight ten nineteen ninety and *yotta*.

In the above sequence the last letter of the previous number is the starting letter for the following number.

Pretty simple answer, but a very clever puzzle.

**Another possible extension is …**

To go one number further with 10^{-18}, *atto*. The sequence thus becomes:

0 1 8 10 19 90 10^{24} 10^{-18}

The addition of atto doesn’t destroy the logic but does make the sequence swing from a purely ascending series to one that descends at the end.

Also because atto ends with *o* you can make the sequence recur with the addition of one to become

0 1 8 10 19 90 10^{24} 10^{-18 }1 8 10 19 90 10^{24} 10^{-18 }…

You can also extend the initial sequence past 90 if you use 10^{-24} which is *yocto*, and it is also recursive with

one … yocto … one … yocto …

All of the additional numbers are on wikipedia at http://en.wikipedia.org/wiki/Yotta