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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.*