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The following spiral sequence of squares is drawn on an infinite blackboard: The

1

st square

(1 \times 1)

has a common vertical side with the

2

nd square (also

1\times 1

) drawn on the right side of it; the 3rd square

(2 \times 2)

is drawn on the upper side of the

1

st and 2nd ones; the

4

th square

(3 \times 3)

is drawn on the left side of the

1

st and

3

rd ones; the

5

th square

(5 \times 5)

is drawn on the bottom side of the

4

th, 1st and

2

nd ones; the

6

th square

(8 \times 8)

is drawn on the right side, and so on. Each of the squares has a common side with the rectangle consisting of squares constructed earlier. Prove that the centres of all the squares except the

1

st lie on two straight lines.
(A Andjans, Riga)

(350) 2

Problems(1)