MathDB

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

Problem Statement