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 [quote="mathgrant"]Glow Artisan is a Nintendo DSi title I just discovered. The game is played on a 5x5 or 12x10 board, which starts out colorless. At the left of each row and the top of each column is an Emitter; your goal is to use these Emitters to recreate the given grid, which contains squares of various colors. You can perform the following moves: * Using an Emitter, you can draw red, yellow, or blue in some number of cells in that Emitter's row or column. These cells must lie in an uninterrupted horizontal or vertical line from the Emitter (so you can add the color to the first three cells in a row, but not three arbitrary cells in that row). If the cells you're drawing on already have a color, the colors will become mixed -- red and yellow make orange, red and blue make purple, yellow and blue make green, and the three colors together make white. There are no "shades" of color besides these 7 colors, so if you draw red on an orange, purple, or white cell, nothing happens to that cell. * You can erase the ENTIRE contents of a row or column, making it colorless again. For example, to create this grid: [code] 12345 vvvvv 1>.PRRR 2>RPRO. 3>RPRY. 4>OWY.. 5>RB... Key: . grey W white R red O orange Y yellow P purple B blue G green[/code] One might first color the entirety of column 1 red and the first three cells of column 4 yellow, and then erase row 1. (I will refer to these moves as C1R5 [for column 1, 5 red cells], C4Y3, and R1X, respectively.) Then perform C2R4, C3R3, C4R2, C5R1, R4Y3 and C2B5 to finish the puzzle in 9 moves, and with 26 cells painted. (Erasures don't count as painting, of course.) Solve this puzzle in the minimum number of moves, and in the minimum number of blocks painted. (They may not necessarily be the same solution.) [code] 12345 vvvvv 1>YPYPY 2>PYPYP 3>YPYPY 4>PYPYP 5>YPYPY Key: . grey W white R red O orange Y yellow P purple B blue G green[/code] (I'm no good at optimizing things, but I get [spoiler]41[/spoiler] moves and [spoiler]75[/spoiler] blocks.)[/quote]
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lostdummy
Posted: Sun Jan 31, 2010 4:41 pm    Post subject: 1

Well, I get same number of moves ( 41 = 3*7 for YPYPY +2*8 for PYPYP + 4 Erases ) just using most obvious solution - doing columns one by one from right to left.

I did fast estimate of "search space" size and it seemed too large for any easy brute force computation (branching factor 160, and number of possible boards 8^25), so I did not try to find better one with program ;p
mathgrant
Posted: Sun Jan 31, 2010 5:24 am    Post subject: 0

Glow Artisan is a Nintendo DSi title I just discovered.

The game is played on a 5x5 or 12x10 board, which starts out colorless. At the left of each row and the top of each column is an Emitter; your goal is to use these Emitters to recreate the given grid, which contains squares of various colors. You can perform the following moves:

* Using an Emitter, you can draw red, yellow, or blue in some number of cells in that Emitter's row or column. These cells must lie in an uninterrupted horizontal or vertical line from the Emitter (so you can add the color to the first three cells in a row, but not three arbitrary cells in that row). If the cells you're drawing on already have a color, the colors will become mixed -- red and yellow make orange, red and blue make purple, yellow and blue make green, and the three colors together make white. There are no "shades" of color besides these 7 colors, so if you draw red on an orange, purple, or white cell, nothing happens to that cell.
* You can erase the ENTIRE contents of a row or column, making it colorless again.

For example, to create this grid:
Code:
12345
vvvvv
1>.PRRR
2>RPRO.
3>RPRY.
4>OWY..
5>RB...

Key:
. grey   W white
R red    O orange
Y yellow P purple
B blue   G green

One might first color the entirety of column 1 red and the first three cells of column 4 yellow, and then erase row 1. (I will refer to these moves as C1R5 [for column 1, 5 red cells], C4Y3, and R1X, respectively.) Then perform C2R4, C3R3, C4R2, C5R1, R4Y3 and C2B5 to finish the puzzle in 9 moves, and with 26 cells painted. (Erasures don't count as painting, of course.)

Solve this puzzle in the minimum number of moves, and in the minimum number of blocks painted. (They may not necessarily be the same solution.)
Code:
12345
vvvvv
1>YPYPY
2>PYPYP
3>YPYPY
4>PYPYP
5>YPYPY

Key:
. grey   W white
R red    O orange
Y yellow P purple
B blue   G green

(I'm no good at optimizing things, but I get 41 moves and 75 blocks.)