500

Part of 1989 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 500 All Soviet Union MO 1989 insects jumps on a square ceiling

Source:

An insect is on a square ceiling side

1

. The insect can jump to the midpoint of the segment joining it to any of the four corners of the ceiling. Show that in

8

jumps it can get to within

1/100

of any chosen point on the ceiling

geometrycombinatoricsdistance