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    I solved this graphically - use nodes to represent the results of calculations and edges to represent operations that can be done on those numbers, then use a graph search algorithm to find the desired path Commented Oct 9, 2013 at 20:22
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    From a reading of the rules, it would seem that it is possible to not reach a perfect solution - for example if the numbers selected are (1, 1, 2, 2, 3, 3) and the target number is 999. So really the target for any algorithm would be finding the closest possible solution. Commented Oct 11, 2013 at 15:34
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    @ell: Is your graph search solution basically a brute force search? Commented Oct 18, 2013 at 8:40
  • I just used a depth first search in my implementation, but I don't see why something like Dijkstra couldn't be used. Commented Oct 18, 2013 at 16:34
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    We have some similar shows in the States: we stick approximately 6 sub-literate idiots in a house for several weeks and film them talking about each other and yelling at each other. That's about as close as our TV gets to something this intellectual in popular shows. Commented Nov 10, 2013 at 23:09