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| − | I visited the site following the link in your comments on Richard Wiseman's most recent Friday Puzzle solution, and thought I'd see if I could contribute.
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| − | However, I can't contribute a solution because the wiki won't accept a solution that takes more than one line. For example, this doesn't work:
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| − | <pre>{{Solution |
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| − | solution
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| − | over
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| − | multiple
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| − | lines
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| − | }}</pre>
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| − | Pretty much all solutions will require multiple lines, so this is a real problem. I assume a "solution" means an answer with working, whereas an "answer" is just the answer by itself.
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| − | Below is my solution to the "7_orbs" puzzle, which I tried to contribute:
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| − | <small>
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| − | :Let A = set of orbs for which there are 3 or more others the same colour.
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| − | :Let B = set of orbs for which there are 1 or 2 others the same colour.
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| − | :Let X = set of orbs for which there are no others the same colour.
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| − | :Goal is to prove that some orb is in A.
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| − | :Possible combinations:
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| − | :(using the shorthand that A denotes an orb that's in A, etc)
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| − |
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| − | :A A A A A A A
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| − | :A A A A A A X
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| − | :A A A A A B B
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| − | :A A A A A X X
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| − | :A A A A B B B
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| − | :A A A A B B X
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| − | :A A A A X X X
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| − | :Label the orbs 1, 2, 3, 4, 5, 6, 7 and test 1&2, 3&4, 5&6.
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| − | :Comparing the results of testing those three pairs with the possible combinations, you can easily show that:
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| − | :If two tested pairs glow the same colour, all members of those pairs are in A
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| − | :If only one of the three tested pairs glows, members of that pair are in A
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| − | :If two tested pairs glow different colours and the other doesn't glow, orb 7 is in A
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| − | :If no tested pairs glow, orb 7 is in A.
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| − | :In all cases, three tests suffice to prove that some orb is in A.
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| − | :The only other thing required is to prove that two tests are not necessarily sufficient, which is trivial.
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| − | </small>
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| − | Is that the sort of thing you're looking for? [[User:Zerrakhi|Zerrakhi]] 12:16, 11 October 2010 (EDT)
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