6

Part of 1973 Czech and Slovak Olympiad III A

Problems(1)

Length of polygonal chain in square

Source: Czech and Slovak Olympiad 1973, National Round, Problem 6

Consider a square of side of length 50. A polygonal chain

L

is given in the square such that for every point

P

of the square there is a point

Q

of the chain with the property

PQ\le 1.

Show that the length of

L

is greater than 1248.

geometrycombinatorial geometry