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Puzzle for Today

Puzzle No. 377 – Thursday 13 December

Throughout the Christmas period the World Darts Championship is taking place, today is the first day, let’s think about impossible scores. With three scoring darts on a conventional dartboard the lowest possible score is 3 and the highest score is 180. There are some impossible scores like 179. What is the lowest impossible score between 3 and 180?

Today’s #PuzzleForToday has been set by Dr Hugh Hunt from Cambridge University Engineering Department.

Answer: 163

It's all about the spacing between triples. There's always a gap of two. But the bull becomes useful at 170 so that one of the gaps between triples disappears. Then another bull comes into play at 160 so that below 160 there is always a combination of t20 and 50 that fills in the space between adjacent triples.

180 = t20+t20+t20

179 gap

178 gap

177 = t20+t20+t19

176 gap

175 gap

174 = t20+t20+t18

173 gap

172 gap

171 = t20+t20+t17

170 = t20+t20+ 50 in creeps the bull

169 gap

168 = t20+t20+t16

167 = t20+ 50+t19

166 gap

165 = t20+t20+t15

164 = t20+ 50+t18

163 gap

162 = t20+t20+t14

161 = t20+ 50+t17

160 = 50+ 50+t20 another bull can be used

159 = t20+t20+t13

158 = t20+ 50+t16

157 = 50+ 50+t19

There are 9 impossible scores

163 166 169 172 173 175 176 178 179

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