The Game

Placement rules

but to get a lower score, a more balanced approach, and of course no bonus, is called for, such as in this game:



with the remarkably low total of 118 (64-54), by "darth8calculus" (in 2016), surpassing (or is it sub-passing?) a modification by "stanley" (62-58, in 2011) of a 62-59 game discovered by "rubik87" in early 2009.

In the normal course of play, on rare occasions there is no place for the 2-piece, or even more rarely, the 1 piece. Here are a couple of "games" where all the pieces are played, but there is no spot for ANY of those pieces:

• The 'largest' possible game consists of playing all the pieces of all the sets (356 squares).
  Fitting all the Blokus pieces can be done on significantly smaller boards than the standard playing board of 400 squares (20x20).

  It can be done on 19x19 (361) or 18x20 (360) boards, which have just 5 or 4 unused squares. In 2007, a 21x17 with just ONE unused square was discovered, as was a 21x16 with NO empty space (but without the four "I" pentominoes).
  In December, 2009, two more 21x17's were found. These two differ only the middle, where the yellow square and Z are switched, along with red 1, 2, and I3 pieces. This yields one symmetric and one slightly asymmetric solution. Asymmetric solutions are much more difficult to find.

  In 2008, enlisting computer assistance, I found 13x14, 12x15, and 10x18 solutions for two colors. (With the 13x14's fleshed out in 2014.) These have just 4 and 2 empty squares, respectively. The latter two can be duplicated to produce 15x24 (or more 18x20) solutions for four colors, also filling 360 squares.

  In 2016, Evan O'Dorney asked about filling 12x14 with 2 colors, omitting the I5's. The results are HERE.

  In 2011, I returned to the one-color challenge, a problem which proved too much for a simple minded computer search: there are simply too many possibilities. Here are some of the by-hand results in 150, 152, 153, 154, and 156 squares: 1-color solutions
  (thanks to mike_yosuke for the most difficult 152).
  
  For those smaller boards, general solving is very difficult: it seems that there is always a piece or two left at the end which won't fit. (I have found such a four-color solution for 19x19, after many hours of trying.)
  An easier method is to use symmetry: put a mixed, complete set of pieces together (one of each kind), and replicate that configuartion as a quadrant or half of the overall solution. (More information   HERE  )
  

  (Click the space below to see my best efforts. The image cycles with each click through all results, then back to blank.)

  
  
  

• Here is the Most Lopsided Game Possible (218-14). Note that red and blue don't even touch.
• Here are two colors in a 4x47 (188 squares) configuration. These four sections fit together: the first and third are rotational symmetries of each other, and the other two have their own rotational symmetry. Furthermore, the two ends will fit together, so this could done on a cylinder.
• What if you are constrained to play the monominoes (single-square pieces) in the corners of the board ?
• What configurations can be created, using (2,3,4 colors) with no empty squares ?
• What is the largest of those ?
• Another puzzle, suggested by "stanley" is to cover as many squares as possible without pieces touching at all.
  Here is a solution which covers 184 squares:
  (186 is also possible, but not in such a symmetric fashion)
  
  Here is a minimal "covering" with just 63 squares occupied:
  In late 2015, "stanley" improved this to 60 squares by placing only the straight pieces in parallel rows, starting 1 row from the edge and putting them 3 rows apart.
  
  
• What other questions might be posed ?
• Solutions to a Tetrominoes Puzzle