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Source: Ukraine 2005 grade 9

July 26, 2009

combinatorics unsolvedcombinatorics

Problem Statement

Under the rules of the "Sea battle" game (no two ships may have a common point), can the following sets of rectangular ships be arranged on a

10 \times 10

square board:

(a)

two ships

1 \times 4

,

4

ships

1 \times 3

,

6

ships

1 \times 2

, and

8

ships

1 \times 1

;

(b)

two ships

1 \times 4

,

4

ships

1 \times 3

,

6

ships

1 \times 2

,

6

ships

1 \times 1

, and

1

ship

2 \times 2

;

(c)

two ships

1 \times 4

,

4

ships

1 \times 3

,

6

ships

1 \times 2

,

4

ships

1 \times 1

, and

2

ships

2 \times 2

?

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