User talk:Oscarlevin

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.

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:

{{Solution | 
solution
over
multiple
lines
}}

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.

Below is my solution to the "7_orbs" puzzle, which I tried to contribute:

Let A = set of orbs for which there are 3 or more others the same colour.

Let B = set of orbs for which there are 1 or 2 others the same colour.

Let X = set of orbs for which there are no others the same colour.

Goal is to prove that some orb is in A.

Possible combinations:

(using the shorthand that A denotes an orb that's in A, etc)

A A A A A A A

A A A A A A X

A A A A A B B

A A A A A X X

A A A A B B B

A A A A B B X

A A A A X X X

Label the orbs 1, 2, 3, 4, 5, 6, 7 and test 1&2, 3&4, 5&6.

Comparing the results of testing those three pairs with the possible combinations, you can easily show that:

If two tested pairs glow the same colour, all members of those pairs are in A

If only one of the three tested pairs glows, members of that pair are in A

If two tested pairs glow different colours and the other doesn't glow, orb 7 is in A

If no tested pairs glow, orb 7 is in A.

In all cases, three tests suffice to prove that some orb is in A.

The only other thing required is to prove that two tests are not necessarily sufficient, which is trivial.

Is that the sort of thing you're looking for? Zerrakhi 12:16, 11 October 2010 (EDT)