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We have a 5x5 grid, on which we can place colored tiles, one by one. The goal is to create a grid with the highest amount of points.

The tile colors are:

  • Blue (1 pt)
  • Red (2 pt)
  • Green (3 pt)
  • Yellow (4 pt)

To place a tile they have to follow the following rules:

  • Blue: Can be placed anywhere.
  • Red: Has to border atleast one blue tile.
  • Green: Has to border one blue and one red tile.
  • Yellow: Has to border one blue, one red, and one green tile.

Other important factors:

  • Bordering, means only the tiles to the nort, east, south and west (no diagonals).
  • Tiles can replace previously placed tiles.
  • We have an infinite amount of tiles.
  • The rules are for placement only. Once a tile has been successfully placed, it's neigbours don't matter anymore.

What is the highest score you can get?

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  • $\begingroup$ This puzzle is based on the game Tower-bloxx, which has been taunting me for way too long, so I hope you guys come up with some good solutions. $\endgroup$ – ThatOneGuy Feb 14 '15 at 11:19
  • $\begingroup$ Googling gave me this page. One guy posted his best there. Just view a spoiler and you'll see it. $\endgroup$ – Spikatrix Feb 14 '15 at 12:04
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I've got a total of 81 points using the following layout:

G Y R Y G
Y G Y G Y
R Y B Y R
Y G Y G Y
G Y R Y G

How? Here is how:

  1. First fill the corners of the 5x5 grid with GREEN tiles by using blue and red tiles adjacent to them at appropriate places. Now ignore the blue and red tiles. The grid is now

G ? ? ? G
? ? ? ? ?
? ? ? ? ?
? ? ? ? ?
G ? ? ? G

  1. Then, place YELLOW tiles adjacent to the green tiles by placing blue and red tiles at appropriate places. Ignore the red and blue tiles placed. The grid is now

G Y ? Y G
Y ? ? ? Y
? ? ? ? ?
Y ? ? ? Y
G Y ? Y G

  1. Now, place a RED tile between two yellow tiles by placing a blue tile at appropriate places. Ignore the blue tiles. The grid is now

G Y R Y G
Y ? ? ? Y
R ? ? ? R
Y ? ? ? Y
G Y R Y G

  1. Now, place GREEN tiles adjacent to two yellow tiles by using blue and red tiles at appropriate positions. Ignore the blue and red tiles placed just now. The grid is now

G Y R Y G
Y G ? G Y
R ? ? ? R
Y G ? G Y
G Y R Y G

  1. Finally place a BLUE tile at the center of the grid and fill the rest of the positions with YELLOW tiles and the grid will be

G Y R Y G
Y G Y G Y
R Y B Y R
Y G Y G Y
G Y R Y G

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  • $\begingroup$ I believe you have misinterpreted/misunderstood the question... It clearly says, and I quote "To place a tile they have to follow the following rules: Blue: Can be placed anywhere. Red: Has to border at least one blue tile. Green: Has to border one blue and one red tile. Yellow: Has to border one blue, one red, and one green tile. Other important factors: Bordering, means only the tiles to the north, east, south and west (no diagonals). Tiles can replace previously placed tiles. We have an infinite amount of tiles." And if you go by the rules given....your answer is wrong. $\endgroup$ – The Dragonista Feb 14 '15 at 14:20
  • $\begingroup$ @TheDragonista , I've said to ignore some tiles after each step in order to make things simpler and the grid, cleaner. And tiles can replace other tiles mean that in order , to construct a tile, say green, one needs a blue and red tile around it. Once placed, the red and/or blue can be replaced with any other tile but that does not mean that the green has to be removed. BTW , haven't you played TowerBloxx? $\endgroup$ – Spikatrix Feb 14 '15 at 14:55
  • $\begingroup$ @Cool Guy Your reds don't border blues, your solution is incorrect. $\endgroup$ – warspyking Feb 14 '15 at 16:54
  • $\begingroup$ Unless i'm missing something, Cool Guys solution is correct. The rules are for placement only, once a tile has been placed it doesn't matter what borders it anymore. I'll add it to the question to make it more clear. $\endgroup$ – ThatOneGuy Feb 14 '15 at 17:38
  • $\begingroup$ @warspyking , I've already mentioned to place blue tiles at appropriate spots so that one can place red tiles between the yellow ones in step 3. $\endgroup$ – Spikatrix Feb 15 '15 at 3:46

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