# 5 Isolated Solutions

Solution #1

The coordinates of the pieces in Mathematica format:

{{{0,0,0},{0,0,1},{0,0,2},{0,0,3},{1,0,2}}, {{0,0,4},{0,1,4},{0,2,4},{0,3,4},{0,2,3}},{{0,1,0},{0,1,1},{0,1,2},{0,1,3},{1,1,1}}, {{1,1,0},{1,2,0},{1,3,0},{1,4,0},{0,2,0}}, {{0,2,1},{1,2,1},{2,2,1},{3,2,1},{2,2,2}},

{{0,3,0},{0,3,1},{0,3,2},{0,3,3},{0,2,2}}, {{0,4,0},{0,4,1},{0,4,2},{0,4,3},{1,4,1}}, {{0,4,4},{1,4,4},{2,4,4},{3,4,4},{1,4,3}}, {{1,0,0},{2,0,0},{3,0,0},{4,0,0},{2,1,0}}, {{1,0,1},{2,0,1},{3,0,1},{4,0,1},{2,1,1}},

{{1,0,3},{2,0,3},{3,0,3},{4,0,3},{2,0,2}}, {{1,0,4},{1,1,4},{1,2,4},{1,3,4},{1,2,3}}, {{1,1,2},{1,2,2},{1,3,2},{1,4,2},{2,3,2}}, {{1,1,3},{2,1,3},{3,1,3},{4,1,3},{2,1,2}}, {{1,3,1},{2,3,1},{3,3,1},{4,3,1},{2,3,0}},

{{1,3,3},{2,3,3},{3,3,3},{4,3,3},{3,4,3}}, {{2,0,4},{2,1,4},{2,2,4},{2,3,4},{2,2,3}}, {{3,1,0},{3,2,0},{3,3,0},{3,4,0},{2,2,0}}, {{2,4,0},{2,4,1},{2,4,2},{2,4,3},{3,4,1}}, {{3,0,2},{3,1,2},{3,2,2},{3,3,2},{3,1,1}},

{{3,0,4},{3,1,4},{3,2,4},{3,3,4},{3,2,3}}, {{4,4,1},{4,4,2},{4,4,3},{4,4,4},{3,4,2}}, {{4,0,2},{4,1,2},{4,2,2},{4,3,2},{4,1,1}}, {{4,0,4},{4,1,4},{4,2,4},{4,3,4},{4,2,3}}, {{4,1,0},{4,2,0},{4,3,0},{4,4,0},{4,2,1}}}

Solution #2

{{{0,0,0},{0,1,0},{0,2,0},{0,3,0},{0,1,1}}, {{0,0,1},{1,0,1},{2,0,1},{3,0,1},{2,0,0}}, {{0,0,2},{0,1,2},{0,2,2},{0,3,2},{0,2,3}}, {{0,0,3},{1,0,3},{2,0,3},{3,0,3},{1,0,2}}, {{0,0,4},{1,0,4},{2,0,4},{3,0,4},{2,1,4}},

{{1,1,1},{1,1,2},{1,1,3},{1,1,4},{0,1,3}}, {{0,1,4},{0,2,4},{0,3,4},{0,4,4},{0,3,3}}, {{0,2,1},{1,2,1},{2,2,1},{3,2,1},{2,2,2}}, {{0,4,0},{0,4,1},{0,4,2},{0,4,3},{0,3,1}}, {{1,0,0},{1,1,0},{1,2,0},{1,3,0},{2,2,0}},

{{1,3,1},{1,3,2},{1,3,3},{1,3,4},{1,2,2}}, {{1,2,3},{2,2,3},{3,2,3},{4,2,3},{3,1,3}}, {{1,2,4},{2,2,4},{3,2,4},{4,2,4},{3,1,4}}, {{1,4,0},{2,4,0},{3,4,0},{4,4,0},{2,3,0}}, {{1,4,1},{2,4,1},{3,4,1},{4,4,1},{2,3,1}},

{{1,4,2},{2,4,2},{3,4,2},{4,4,2},{2,3,2}}, {{1,4,3},{2,4,3},{3,4,3},{4,4,3},{2,3,3}}, {{1,4,4},{2,4,4},{3,4,4},{4,4,4},{2,3,4}}, {{2,1,0},{2,1,1},{2,1,2},{2,1,3},{2,0,2}},{{3,0,0},{3,1,0},{3,2,0},{3,3,0},{3,1,1}},

{{4,0,1},{4,0,2},{4,0,3},{4,0,4},{3,0,2}}, {{4,1,1},{4,1,2},{4,1,3},{4,1,4},{3,1,2}}, {{3,3,1},{3,3,2},{3,3,3},{3,3,4},{3,2,2}}, {{4,0,0},{4,1,0},{4,2,0},{4,3,0},{4,2,1}}, {{4,3,1},{4,3,2},{4,3,3},{4,3,4},{4,2,2}}}

Solution #3

{{{0,0,0},{1,0,0},{2,0,0},{3,0,0},{2,1,0}}, {{0,0,1},{1,0,1},{2,0,1},{3,0,1},{2,1,1}}, {{0,0,2},{1,0,2},{2,0,2},{3,0,2},{2,1,2}}, {{0,0,3},{1,0,3},{2,0,3},{3,0,3},{2,1,3}}, {{0,0,4},{1,0,4},{2,0,4},{3,0,4},{2,1,4}},

{{0,1,0},{0,1,1},{0,1,2},{0,1,3},{0,2,2}}, {{0,1,4},{0,2,4},{0,3,4},{0,4,4},{0,2,3}}, {{0,2,0},{1,2,0},{2,2,0},{3,2,0},{1,3,0}}, {{0,2,1},{1,2,1},{2,2,1},{3,2,1},{2,2,2}}, {{0,3,0},{0,3,1},{0,3,2},{0,3,3},{1,3,1}},

{{0,4,0},{0,4,1},{0,4,2},{0,4,3},{1,4,2}}, {{1,1,0},{1,1,1},{1,1,2},{1,1,3},{1,2,2}}, {{1,1,4},{1,2,4},{1,3,4},{1,4,4},{1,3,3}}, {{1,2,3},{2,2,3},{3,2,3},{4,2,3},{3,2,2}}, {{2,3,1},{2,3,2},{2,3,3},{2,3,4},{1,3,2}},

{{1,4,0},{2,4,0},{3,4,0},{4,4,0},{2,3,0}}, {{1,4,1},{2,4,1},{3,4,1},{4,4,1},{2,4,2}}, {{1,4,3},{2,4,3},{3,4,3},{4,4,3},{2,4,4}}, {{3,1,4},{3,2,4},{3,3,4},{3,4,4},{2,2,4}}, {{3,1,0},{3,1,1},{3,1,2},{3,1,3},{4,1,1}},

{{3,3,0},{3,3,1},{3,3,2},{3,3,3},{3,4,2}}, {{4,0,0},{4,1,0},{4,2,0},{4,3,0},{4,2,1}}, {{4,0,1},{4,0,2},{4,0,3},{4,0,4},{4,1,3}}, {{4,1,2},{4,2,2},{4,3,2},{4,4,2},{4,3,1}}, {{4,1,4},{4,2,4},{4,3,4},{4,4,4},{4,3,3}}}

Solution #4

{{{0,0,0},{0,1,0},{0,2,0},{0,3,0},{0,1,1}}, {{0,0,1},{1,0,1},{2,0,1},{3,0,1},{2,0,0}}, {{0,0,2},{0,1,2},{0,2,2},{0,3,2},{0,1,3}}, {{0,0,3},{1,0,3},{2,0,3},{3,0,3},{2,0,2}}, {{0,0,4},{1,0,4},{2,0,4},{3,0,4},{2,1,4}},

{{0,1,4},{0,2,4},{0,3,4},{0,4,4},{0,2,3}}, {{0,2,1},{1,2,1},{2,2,1},{3,2,1},{2,2,2}}, {{0,3,1},{1,3,1},{2,3,1},{3,3,1},{2,3,0}}, {{0,3,3},{1,3,3},{2,3,3},{3,3,3},{1,4,3}}, {{0,4,0},{0,4,1},{0,4,2},{0,4,3},{1,4,1}},

{{1,0,0},{1,1,0},{1,2,0},{1,3,0},{1,1,1}}, {{1,0,2},{1,1,2},{1,2,2},{1,3,2},{1,1,3}}, {{1,1,4},{1,2,4},{1,3,4},{1,4,4},{2,3,4}}, {{1,2,3},{2,2,3},{3,2,3},{4,2,3},{2,2,4}},{{1,4,0},{2,4,0},{3,4,0},{4,4,0},{3,4,1}},

{{2,4,1},{2,4,2},{2,4,3},{2,4,4},{1,4,2}}, {{2,1,0},{2,1,1},{2,1,2},{2,1,3},{3,1,1}}, {{3,0,0},{3,1,0},{3,2,0},{3,3,0},{2,2,0}}, {{3,1,2},{3,2,2},{3,3,2},{3,4,2},{2,3,2}}, {{4,0,1},{4,0,2},{4,0,3},{4,0,4},{3,0,2}},

{{4,1,1},{4,1,2},{4,1,3},{4,1,4},{3,1,3}}, {{3,1,4},{3,2,4},{3,3,4},{3,4,4},{4,2,4}}, {{4,4,1},{4,4,2},{4,4,3},{4,4,4},{3,4,3}}, {{4,0,0},{4,1,0},{4,2,0},{4,3,0},{4,2,1}}, {{4,3,1},{4,3,2},{4,3,3},{4,3,4},{4,2,2}}}

Solution #5

{{{0,0,0},{0,0,1},{0,0,2},{0,0,3},{1,0,2}}, {{0,0,4},{0,1,4},{0,2,4},{0,3,4},{0,2,3}}, {{0,1,0},{0,2,0},{0,3,0},{0,4,0},{0,3,1}}, {{0,1,1},{1,1,1},{2,1,1},{3,1,1},{1,0,1}}, {{0,1,2},{0,2,2},{0,3,2},{0,4,2},{0,3,3}},

{{0,1,3},{1,1,3},{2,1,3},{3,1,3},{2,1,4}}, {{0,2,1},{1,2,1},{2,2,1},{3,2,1},{2,2,2}}, {{0,4,1},{1,4,1},{2,4,1},{3,4,1},{2,4,2}}, {{0,4,3},{1,4,3},{2,4,3},{3,4,3},{1,3,3}}, {{0,4,4},{1,4,4},{2,4,4},{3,4,4},{2,3,4}},

{{1,0,0},{2,0,0},{3,0,0},{4,0,0},{3,0,1}}, {{2,0,1},{2,0,2},{2,0,3},{2,0,4},{1,0,3}}, {{1,0,4},{1,1,4},{1,2,4},{1,3,4},{2,2,4}}, {{1,1,0},{1,2,0},{1,3,0},{1,4,0},{1,3,1}}, {{1,1,2},{1,2,2},{1,3,2},{1,4,2},{2,3,2}},

{{1,2,3},{2,2,3},{3,2,3},{4,2,3},{2,3,3}}, {{2,1,0},{2,2,0},{2,3,0},{2,4,0},{2,3,1}}, {{3,0,2},{3,1,2},{3,2,2},{3,3,2},{2,1,2}}, {{4,0,1},{4,0,2},{4,0,3},{4,0,4},{3,0,3}}, {{3,0,4},{3,1,4},{3,2,4},{3,3,4},{4,2,4}},

{{3,1,0},{3,2,0},{3,3,0},{3,4,0},{3,3,1}}, {{4,3,1},{4,3,2},{4,3,3},{4,3,4},{3,3,3}}, {{4,4,1},{4,4,2},{4,4,3},{4,4,4},{3,4,2}}, {{4,1,0},{4,2,0},{4,3,0},{4,4,0},{4,2,1}}, {{4,1,1},{4,1,2},{4,1,3},{4,1,4},{4,2,2}}}

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