**The Triplication Problem**

There is a total number of 14070 solutuions to this problem with rotations and reflections not counted as distinct. The number of solutions for each triplication is listed below. For each piece the total number of solutions is given and the number of solutions for each set of three pentominoes omitted is also given.

F - 443 Solutions

I - 201 Solutions

L - 938 Solutions

P - 9144 Solutions.

N – 610 Solutions

T – 382 Solutions

U – 444 Solutions

V – 482 Solutions

W – 202 Solutions

X - 20 Solutions

Y – 809 Solutions

Z – 395 Solutions

If we look for sets of pentominoes which can triplicate all 12 pieces then we find there are only five possible sets. These are shown here together with the total number of solutions for each set.

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