Four-by-Four Skyscrapers

Place a building of height 1, 2, 3 or 4 in each cell of a $4 \times 4$ grid so that every row and every column contains each height exactly once. A number on the edge of the grid says how many buildings are visible when you look along that row or column from that side; a taller building hides every shorter building behind it. The given clues are: - Looking down column 3 from the top: 1 building. - Looking down column 4 from the top: 2 buildings. - Looking up column 1 from the bottom: 2 buildings. - Looking up column 4 from the bottom: 1 building. - Looking along row 2 from the left: 1 building. - Looking along row 2 from the right: 3 buildings. Give the top row as a four-digit number, reading left to right.

• graph theory

Source: Skyscrapers (Towers) puzzles are a well-known Latin-square variant in wide circulation; this instance was written for AxiomIQ.