A torpedo set consists of $2$ pieces of $1 \times 4$, $4$ pieces of $1 \times 3$, $6$ pieces of $1 \times 2$ and $ 8$ pieces of $1 \times 1$ ships. a) Can one put the whole set to a $10 \times 10$ table so that the ships do not even touch with corners? (The ships can be placed both horizontally and vertically.) b) Can we solve this problem if we change $4$ pieces of $1 \times 1$ ships to $3$ pieces of $1 \times 2$ ships? c) Can we solve the problem if we change the remaining $4$ pieces of $1 \times 1$ ships to one piece of $1 \times 3$ ship and one piece of $1 \times 2$ ship? (So the number of pieces are $2, 5, 10, 0$.)