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Mathé's 2-Angel proof is really nice, or at least the summary is appealing -- he imagines a 'nice' devil, shows it can be beaten, then proves that if you can be
by vessenes 11y ago
Mathé's 2-Angel proof is really nice, or at least the summary is appealing -- he imagines a 'nice' devil, shows it can be beaten, then proves that if you can beat the nice devil, you can beat the mean one.
This is one of my favorite problem solving strategies -- reducing to a more obvious solvable situation, then filling in the chinks and gaps to expand back.
- dsp1234 11y agoThe Kloster solution[0] solves it in a more direct way, by showing that for each action the devil takes the angel can take a counter action by limiting it's own moves. In the one proof is the realization that sometimes it's easier to solve a smaller problem then prove equivalence to a harder problem, and in the other is the realization that sometimes voluntarily reducing the number of actions can lead to a simpler solution. Both are pretty good tools to have under one's belt. [0] - http://home.broadpark.no/~oddvark/angel/kloster.html http://home.broadpark.no/~oddvark/angel/kloster.html