Brain warm-up B (Boom)

[EvilAndrew]

For the start of the semester, I have decided to give everyone a quick brain warm-up. Feel free to e-mail me your solutions (my SIUE address starts with â€Ã...“rlamoni@â€Ã,) I will post a reply to this message with the names (or pseudonyms if desired) of the correct submitters in a day or two or when a sufficient number of people have answered the question. At that point, I will add a new question. Each question will have a title that could be a clue or just an inside joke. ;-)

Please DO NOT reply to the tread with an answer to the problem. E-mail it instead.

[EvilAndrew]

Brain warm-up B (Boom)
   The following sets of characters represent games of minesweeper.  Each number represents the number of mines that are adjacent (horizontally, vertically, or diagonally) to it.  Your job is to replace ten of the question-marks in each set with one mine each to prove the numbers accurate.  There is only one possible solution for each set.  

1?1????1    ????????
?11111?1    0?1?0??1
1?1????1    ??1??1??
?1??1?1?    ??????1?
?1??1??1    ?3?2?1?0
??1???1?    ?????2??
1??????1    ??13????
?1?1?1??    ?0????0?

Send your solutions with a * for each of the ten mines.  If you can only solve one of the two problems, then send the answer anyway.

Because the above Pictures are ugly here is another version.

[EvilAndrew]

So far, 4 people have solved Board #1 and 3 people have solved Board #2.  I think five is a good number, but I don’t want to wait too long.  

The next puzzle is called Counterfeit Coins and it is (in case you could not guess) a â€Ã...“Find the fake Coins using a scaleâ€Ã, puzzle.

I am going to post the answer to Boom and the solver's names at noon on Thursday. So get your answers in quick.

[EvilAndrew]

Solvers:
1. tom von kercey (solved: 1-12-2005 12:09pm)
2. Steve Klein (solved: 1-12-2005 3:23pm)
3. sunil (solved: 1-12-2005 4:24pm)
4. Erin Harris (solved: 1-12-2005 4:37pm)
5. Pete Lamonica (solved: 1-12-2005 11:21pm)

Answers:
1?1*??*1 ??*?????
*11111?1 0?1?0??1
1?1????1 ??1??1*?
?1?*1?1* *??*??1?
*1??1??1 *3?2*1?0
??1???1? *????2??
1??*?*?1 ??13*???
*1?1?1?* ?0?**?0?


Strategy:
On Board #1, a good strategy is to find places that that mines cannot possibly go first.  For example, there must be a mine in (1,2) or (2,1) to satisfy the (1,1) square,  Thus there cannot be a mine in (3,1) because both (1,2) and (2,1) are adjacent to (2,2).  There cannot be a mine in (3,7) because then (1,8) could not be satisfied without violating (2,8).  I could go on and on, but eventually you will X-out enough squares that a few mines are forced.  If you keep track of the â€Ã...“must be here or hereâ€Ã, rules then a chain reaction usually results.  I was not able to chain reaction the entire problem one, but I did reach a point where many 1’s had to be covered by just a few mines and so their locations were the obviously central ones.

Board #2 has some extra help in the form of 0’s.  0’s can have all their adjacent squares marked mine-less immediately.  Another helpful hint to use on this board is the â€Ã...“there is only one solution rule.â€Ã,  This rule means that any time you could have a mine in more then one place without making a difference to the rest of the puzzle then those places must either be completely filled with mines of devoid of them because there is â€Ã...“only one solutionâ€Ã,.  The comes into play with the 3 in (5,2) A mine could go in (4,1), (5,1), or (6,1) and not be adjacent to any other numbered squares.  This means that these three squares must be empty or full of mines.  Thus, if you reach a point (as I did) in which there are no longer three available spaces to the right, top or bottom of the 3 you can now be sure that all three of the above mentioned squares should be filled.  This pattern occurs in other places as well.