Problems on squared paper

16

TASKS
ON PAPER
IN THE CAGE

1. How many squares?

The knots of a piece of checkered paper form a cross, as shown in figure.

How many squares can you draw with vertices at the selected nodes?

(For details, see page 50.)

2. How many rectangles?

At figure you see a square piece of checkered paper. Let’s count how many squares with vertices can be formed

at the nodes of this sheet and with sides parallel to its sides.

Obviously, the number of possible “unit” squares is $n^2$. Squares of size $2 \times 2$ will be found $(n-1)^2$. Indeed, the upper left corner of such a square can be in any

(Continued on page 54.)