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I recently travelled from my home town to a distant music concert, on a pedal tricycle of all things! My wonderful, three wheeled tricycle.
I knew that the epic 2,345 mile trip would wreak havoc on the tyres, but luckily I took along 4 spares!
Instead of waiting for any single tyre to fail, I decided that I would rotate the tyres evenly, making sure that by the end of the trip all seven tyres had travelled exactly the same distance.
Hint: Think of the pages from 19, and then 1099.
Answer: There are 147 pages and the number 3 appears 35 times.
Stage 1
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For pages 1  9 we have a total of 9 digits. For pages 10  99 we have a total of 180 digits. This is a total so far of 189, therefore we require another 144 digits, which is another 48 pages. Taking us to 147 pages in total.
Stage 2
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From page 1 to 147 we have 15 times where the page number ends in 3. We also have the ten pages in the 30's, and the ten pages in the 130's that have the extra 3 in them. For a total of 35 number 3s.
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