Printing Error
Every third page number in this book has been omitted. Can you work out what number will be on the last page?
Age
11 to 14
Challenge level
Problem
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.
Student Solutions
Answer: 133
| page | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| number | 1 | 2 | 4 | 5 | 7 | 8 | 10 | |||
| = | = | +1 | +1 | +2 | +2 | +3 | +3 | +4 | +4 |
Add one to the difference for each odd page
89 is before 90, the 45th even number, so 89 is the 45th odd number
Difference has increased by 1 for every odd number except for 1
So number 89 + 45 = 133 is printed on the last page.