XPost: alt.fan.cecil-adams

On Sat, 12 Sep 2015 13:40:59 -0400, ebenZEROONE@verizon.net (Hactar) wrote:

My mom made me a tetromino[1]-piece bday cake. Very cool. But she
couldn't find a way to cut a 4x6 cake into six different pieces. I can't >either. Can anyone here? Here's the pieces she used:

1111 (blue)

222
2 (green)

3
333 (grey)

44
44 (yellow)

5
55
5 (pink)

66
66 (brown)

proposed mirror-image replacement:
77
77

Not possible with pieces 1 through 6; replacing 6 with 7 does not bring joy.

Color the 4x6 cake with a checkerboard pattern of alternating colors. Twelve squares will be color A (say black) and twelve will be color B (say red). Now color the individual pieces a checkboard pattern of alternating colors. Each piece will add two squares of each color -- except piece 5, which will always have three squares of one color and one square of the other color. So you can't get twelve and twelve with that mix of pieces. The same reasoning applies to all seven pieces in a 4x7 square.

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