Solving Really Hard Puzzles
Black and White, MUMS 2010, puzzle 4.2

This puzzle (available here) is pretty much a grind through it puzzle. We finished in about 1h27m.

I usually hate logic puzzles that require guessing/branching instead of strictly logical steps.  But I got very used to using those tactics with these. Our log is after the cut.

Log:

0:00:00
Opening puzzle
0:00:40
Printing. definitely needs printing.
0:02:04
J: So there are 2 ways to make a 1x1, 3 ways to make a 1x2 and 6 ways to make a 1x3. That gives 26 squares but we only have 5x5 grids. So you won’t use both 1x1s.
0:03:12
J: It’s easy to tell which by counting the number of black and white squares. The 1x1 is probably the letter you pick.
0:03:23
grid 2, there’s only one 3B and one 3W. easy in.
0:03:51
we’re dividing them up. no reason to cooperate.
0:08:03
Solved #2.
0:12:01
J solved 1, I solved 3. we have ONE so far.
0:15:47
Solved 4. M. we have ONEM
0:18:17
Solved 9, R
0:19:13
J: 21T
0:22:47
10I
0:26:45
6R
0:35:39
got 12 U (after struggling with 8 for 6 minutes)
0:36:53
14 P  [This grid was ambiguous, and P was the wrong letter. May have slowed down our wheel-of-fortune-ing some.]
0:40:41
24P, 18C.
0:41:45
J: I figured the pulled out letters would make a new 5x5 square and it would have to be solved the same way. But there aren’t 3 blacks in a row.
0:47:21
17A
0:50:10
11D. A quick note: my solving method is: hopefully a force 1x3 (two, if lucky.) then brute force bifurcation, focusing on the color with only 12, since it can’t have a single.
0:51:11
J: I think it starts ONE MORE GRID
1:00:36
Struggled with 23, finally got I
1:01:29
Could end BLACK STRIPE
1:02:18
we’ll assume BLACK for now and not solve those
1:05:04
13 S. maybe 14 is E
1:06:02
14 is ambiguously P or E. J thinks: ONE MORE GRID USE BLACK STRIPS [J is correct, well done Jonathan!]
1:06:47
J: the black ones are ONMOIDSEACSTR
1:10:56
Maybe we have to put the letters where they came from in their original grid, not where their grid is in the big 5x5  [Well done, Eric. Key aha]
1:11:37
J: or what’s in the 1x3 black strips
1:15:48
No conflicts in the “which square did they come from” meethod so far. .u.A. iC.D. MISe. N.r.E Op.r.
1:16:38
We only need the black letters, so we need to solve 5 20 21 22 
1:16:58
J has more. now we have su.Ab iC.D. MISeg NSr.E Op.rl
1:19:59
Apparently we have all 12 black squares now. su.Ab iC.DO MISeg NSrTE Op.rl where the dots have to be white.
1:21:36
No, there are 13 black squares.
1:24:22
The R from 22 goes top row, middle.
1:24:28
Solving the last grid. suRAb iCkDO MISeg NSrTE Operl
1:26:57
J guessed DOMINO, CORRECT! [I was almost done solving the final grid. He just guessed from eyeballing the black letters. I got the brute force work mostly, J got the educated guessing role.]
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