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A book has $89$ pages, but the page numbers are printed incorrectly. Every third page number has been omitted, so that the pages are numbered $1,2,4,5,7,8,...$ and so on. What is the number on the last printed page?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas. 

This problem is taken from the UKMT Mathematical Challenges.
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