math challenge

Weeks of March 16 - 29, 1998

Tile Tally

Tim, the tile man, has landed a contract to cover the floor of a new software emporium. The eccentric owner has requested a bottom layer of ceramic tiles that measure 50 cm x 50 cm each, and a top layer of carpet squares that measure 60 cm x 60 cm each.

If the floorspace of the emporium is exactly 42 m x 60 m, how many more ceramic tiles than carpet squares will Tim need?

The owner has selected a carpet square with a perfectly-centered, diamond pattern (as shown). If Tim covers the ceramic tiles using these carpet squares, how much of the floorspace will be covered by diamonds?

See the solutions