# Sunday Times Teaser 3126 – Sweet Success

*by Victor Bryant*

#### Published Sunday August 21 2022 (link)

My five nieces Abby, Betty, Cathy, Dolly and Emily each had some sweets. I asked them how many they had but they refused to answer directly. Instead, in turn, each possible pair from the five stepped forward and told me the total number of sweets the two of them had. All I remember is that all ten totals were different, that Abby and Betty’s total of 8 was the lowest, and that Cathy and Dolly’s total of 18 was the second highest. I also remember one of the other totals between those two but I don’t remember whose total it was. With that limited information I have worked out the total number of sweets.

In fact it turns out that the other total I remember was Betty and Cathy’s.

In alphabetical order of their names, how many sweets did each girl have?

Runs a bit faster with PyPy.

better late than never