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Proof with brute-force procedure. Here I used fact that we for sure can cover with 16 pentominoes, so I tried to cover half with 8 or less and then see if two such half-covers cover the whole board. It takes about 15 seconds on my PC to get the answer.

Proof with brute-force procedure. Here I used fact that we for sure can cover with 16 pentominoes, so I tried to cover half with 8 or less and then see if two such half-covers cover the whole board. It takes about 15 seconds on my PC to get the answer.

Proof with brute-force procedure. Here I used fact that we for sure can cover with 16 pentominoes, so I tried to cover half with 8 and then see if two such half-covers cover the whole board. It takes about 15 seconds on my PC to get the answer.

Proof with brute-force procedure. Here I used fact that we for sure can cover with 16 pentominoes, so I tried to cover half with 8 or less and then see if two such half-covers cover the whole board. It takes about 15 seconds on my PC to get the answer.

Proof in code:

Proof with brute-force procedure. Here I used fact that we for sure can cover with 16 pentominoes, so I tried to cover half with 8 and then see if two such half-covers cover the whole board. It takes about 15 seconds on my PC to get the answer.