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#60 Mexican standoff

The Good, the Bad and the Bumbling have decided the only way to resolve their differences is with a three-way duel, aka a Mexican standoff. They stand in a triangle, each armed with a gun and unlimited ammunition. As you might expect, Good has the deadliest shot: he kills his target 99 per cent of the time. Bad is more hit-and-miss: his success rate is 66 per cent. And Bumbling, in his role as the comedy relief, only fatally hits the mark 33 per cent of the time. On a count of three, each will draw their gun and, using the best strategy they can, will keep shooting with the aim of being the last spaghetti westerner standing.

Roughly what is the chance that Bumbling will survive?

Answer next week

#59 Celebrate the differences

Solution

Reading row by row: 374 / 968 / 251. The middle-left number has six connections so it must be 1 or 9, but 1 can be ruled out because it doesn鈥檛 connect to 4鈥檚 neighbours, which must include 7, 8 or 9. By considering the highest possible numbers that circles can now contain, the only places for the 6 are the bottom right (which eventually leaves two low numbers cramped together on the bottom row) or in the centre. The latter case works, but requires 5 in the bottom middle. Using the 鈥淣ot 1鈥� rule fills in the rest.