Product Skyscrapers
Product Skyscrapers is a variation of the classic Skyscrapers puzzle, likely first proposed by Andrey Bogdanov in 2004 for the Internet Puzzle Solvers Test competition. This variant naturally follows the idea introduced by Summed Skyscrapers, extending the clue logic from sums to products.
As in standard Skyscrapers, digits represent building heights and each row and column must contain all heights without repetition. Instead of indicating how many buildings are visible, clues show the product of visible heights from a given direction, introducing a distinct layer of numerical reasoning. The interplay of visibility logic and multiplicative constraints provides elegant and challenging deduction paths.
As in standard Skyscrapers, digits represent building heights and each row and column must contain all heights without repetition. Instead of indicating how many buildings are visible, clues show the product of visible heights from a given direction, introducing a distinct layer of numerical reasoning. The interplay of visibility logic and multiplicative constraints provides elegant and challenging deduction paths.
Rules
Insert a digit from 1 to 5 into every cell, so that each digit appears once in each row and column. Each digit in a cell represents the height of a building. Numbers outside the grid indicate a product of heights of visible buildings a distant observer could see (at least part of) in that row or column. A building will hide any shorter buildings behind it.
Click to see the answer.