Tower Sums

Tower Sums is a grid of city blocks, and you write a tower height into every square. Each row and each column must use every height from 1 up to the grid size exactly once, the way a Sudoku row uses every digit once. The clues sit outside the grid, and each one describes the towers visible when you stand at that edge and look down the line — a taller tower hides every shorter tower behind it.

The clues come in four flavours and this is where the arithmetic enters. A count clue says how many towers you can see. A sum clue gives the total of the visible towers. A product clue gives them multiplied together. A hidden-sum clue gives the total of the towers you cannot see. So on a row of four, a count clue of 1 tells you the tallest tower stands nearest you, and a sum clue of 9 on that same row is a much richer statement — it constrains which towers are visible and therefore the order they stand in.

Every puzzle served has exactly one solution, and it can always be reached by reasoning rather than guessing. It suits students who enjoy Sudoku and are ready for something with more arithmetic in it, roughly upper primary through middle school.