# User talk:Oscarlevin

From Math Puzzle Wiki

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)