What puzzles can be answered without being completely solved, e.g.

logic/answered.not.solved New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

What puzzles can be *answered* without being completely *solved*, e.g.
non-constructively or using the extra assumption that a solution
exists?

Does anyone have examples of puzzle which can be *answered* without
being completely *solved*, e.g. non-constructively or using the extra
assumption that a solution exists?

-- Tal Kubo <kubo@zariski.harvard.edu>, "Easier to Answer than to
   Solve", July 1994

Show solution

For example, a friend of mine was given the following puzzle at a job
interview:  2 players alternate in placing non-overlapping identical
coins on a circular table, and the last player to move wins; which
player has a winning strategy?

One approach to this puzzle is to actually find the winning strategy (a
nice problem).  But there is a shortcut using meta-information implicit
in the question: since nothing is said about the size of the table, we
can assume that it has the same size as the coin, so player 1 wins.
This doesn't give any information at all on what the winning strategy
is, but it suffices to answer the question.

-- Tal Kubo <kubo@zariski.harvard.edu>

[ Editor: no other examples were found in the collected postings.  The
coin game itself is competition/games/cigarettes. ]