Question 5
A dartboard is divided into 20 numbered sectors. Each turn uses 3 darts. A bull (smallest central circle) scores 50; the surrounding half-bull ring scores 25. The unshaded part of a sector scores its number, the outer gray ring doubles it, and the middle gray ring triples it. The black outer area scores 0. The illustrated darts score $25+3\times13+12=76$.
(a) Ruthee scores 137 with two triples and one single, neither bull nor half-bull. Find all ways.
(b) Archie scores 137 with two triples and a double. Find all ways.
(c) Archie throws three darts, each scoring a double or triple. What total scores are impossible?
(a) Ruthee scores 137 with two triples and one single, neither bull nor half-bull. Find all ways.
(b) Archie scores 137 with two triples and a double. Find all ways.
(c) Archie throws three darts, each scoring a double or triple. What total scores are impossible?