Bob is reading a 500 page book, with odd numbered pages on the left, and even numbered pages on the right. Multiple times in the book, the sum of the digits of the two opened pages are 18. Find the sum of the page numbers of the last time this occurs.
See first post, in which we determine that the left hand page ends in 9 and the right hand page in zero. This accounts for 9 of the required 18 SOD.
So, we are looking for two consecutive numbers less than 50 whose SOD adds to nine.
49 and 50 do not work.
48 and 49 have an SOD of 25.
47 and 48 have an SOD of 23, which is 2 less.
46 and 47 have an SOD of 21. which is 2 less.
Now I see the pattern. I want to lose 12, so subtract 6 from each.
40 and 41 have an SOD of 9,
so the last page numbers which sum to 18 SOD are 409 and 410.
And their sum is 819. Final answer.
Solution (Spoiler)
