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In September, my puzzle appeared as Alex Bellos's Monday Puzzle. The puzzle asked what the highest rugby score was which can only be made with one combination of kicks, tries and converted tries.

What is the highest rugby score which can be made with 101 different combinations of kicks, tries and converted tries?

## Rugby Scores

In a rugby (union) match, 3 point are scored for a kick, 5 for a try and 7 for a converted try. This scoring system means that some total scores can be achieved in different combinations, while others can be achieved in only one way.

For example, 14 can be scored in two ways (three kicks and a try; or two converted tries), while 8 can only be achieved in one way (try and a kick).

What is the highest score which can only be made in one way?

What is the highest score which can be made in two ways?