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## 'Lost Books' printed from http://nrich.maths.org/

While we were sorting some papers we found $3$ strange sheets
which seemed to come from small books. They had once been used for
wrapping and one side was very faded. The other side was in a
language we did not know, but there were page numbers at the foot
of each page.

Did the pages come from the same book, we wondered, and what
numbers had been on the other sides of the sheets?

I decided to make a little book to see how the numbers worked.
It had $4$ sheets which I folded to make $16$ pages. There was no
need to staple it.

Then I made other little books, with both more and fewer pages.
I made a table of my results and soon I knew how the numbering
worked and could answer my own questions.

What answers do you think I got?

Later we found another sheet. The numbering on this was a bit
different. Can you work out why?