16. Beth, Carolyn and George love reading their favourite bedtime stories together. They take it in turns to read a page, always in the order Beth, then Carolyn, then George. All twenty pages of the story are read on each occasion. One evening, Beth is staying at Grandma's house but Carolyn and George still read the same bedtime story and take it in turns to read a page with Carolyn reading the first page.
In total, how many pages are read by the person who usually reads that page?
A 1
B 2
C 4
D 6
E 7
Solution: D
When all three children are present, Carolyn reads pages $2,5,8, \ldots$, that is those pages whose number leaves remainder 2 when divided by 3 . George reads pages $3,6,9$, ..that is, those whose number is a multiple of 3 . When Beth stays at Grandma's, Carolyn reads pages $1,3,5, .$. that is the odd numbered pages, and George reads the even numbered pages. So the pages that Carolyn reads both normally and also when Beth is away are those with numbers which have remainder 2 when divided by 3 , and are odd. That is, the three pages 5,11 and 17. The pages that George reads both normally and also when Beth is away are those with numbers that are multiples of 3 and are even, that is, the three pages 6,12 and 18 . So there are altogether 6 pages which are read by the same person normally and when Beth is away, namely pages $5,6,11,12,17$ and 18 .