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Lizely

Skyscrapers Puzzle

Solve a compact, uniquely verified skyline puzzle by placing heights 1 through 4 and satisfying five necessary viewing clues.

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How to use

  1. 1.Select a lot, then enter a height from 1 through 4 with the on-screen controls or keyboard; use arrows to move and Delete to clear.
  2. 2.Place each height exactly once in every row and column, then count visible buildings from each shown edge clue as taller buildings hide shorter ones.
  3. 3.Fill all 16 lots and press Enter or Check skyline; repair the first incorrect completed attempt before a second error deadlocks the run.

About Skyscrapers Puzzle

Skyscrapers, also called Towers, is a Latin-square logic puzzle with a visual twist. Each cell represents a building whose height is a number from 1 through 4. Every row must contain all four heights exactly once, and every column must do the same. Numbers around the outside describe how many buildings can be seen when that line is viewed from that edge. A building is visible only when it is taller than every building before it, so a tall foreground building hides all shorter buildings behind it.

This page publishes one fixed product-authored 4 by 4 puzzle. It is deliberately stable rather than randomly generated, which makes its clues, success route, tests, and accessibility behavior reproducible on every visit. The displayed fixture uses five edge clues. Eleven edge positions are intentionally omitted and shown as quiet dots. An omitted clue imposes no extra condition, but the row and column permutation rules still apply everywhere. The solution and clue subset were created for Lizely and were not copied from either linked rules source.

The clue set is small without being ambiguous. An independent solver generates all 24 permutations of heights 1 through 4 for each row. It filters row candidates against any left or right clue, adds rows through backtracking, and rejects a candidate as soon as it duplicates a height in a column. Top clues provide an additional partial-search bound. At a full grid, the solver validates every row, every column, and all four viewing directions. The release test requires the five published clues to produce exactly one solution.

Sufficiency is only half of the fixture check. The tests also remove each shown clue one at a time and count again. Every removal produces more than one valid grid, demonstrating that each of the five clues contributes information needed for uniqueness. This makes the published set sufficient but nonredundant: it avoids printing extra clues that the other rules already imply. The proof is about this fixed fixture, not a claim that every Skyscrapers puzzle needs five clues.

To play, select a lot and enter a height with the on-screen 1 through 4 controls or the matching number key. Arrow keys move around the grid. Delete or Backspace clears the selected lot. Each row and column must end with one 1, one 2, one 3, and one 4. Then test every shown clue from its own edge. Keep a running maximum while looking inward; count the first building, and add one only when a later height exceeds that maximum.

The boundary clues are useful mental anchors. A clue of 1 means the tallest possible building must stand first from that viewing direction, because it immediately hides every later building. In a four-cell line, a clue of 4 means the heights must rise strictly as 1, 2, 3, 4 from that edge. Other clue values allow several orders. For example, scanning 2, 1, 4, 3 shows two buildings: height 2 is initially visible, height 1 is hidden, height 4 becomes the new maximum, and height 3 is hidden behind it.

Start with the shown clue of 3 on the right side of the fourth row. Three buildings must become visible while scanning that row from right to left, which sharply limits its possible permutations. Next combine the left clue on the second row with the three bottom clues. Whenever a row candidate fixes a height in a column, remove that height from the other cells in the same column. Recheck visibility after each deduction rather than treating clues as totals; visibility depends on order, not on the arithmetic sum of heights.

Choose Check skyline only after all 16 lots are filled. Checking an incomplete grid displays a reminder and does not use a mistake. A completed grid that violates a row, column, or clue records one mistake but remains editable, so you can repair the first attempt. A second incorrect completed check deadlocks the run until Restart. The unique correct grid awards exactly 1,000 points. Completed and deadlocked states are terminal: numbers, clearing, movement, selection, and additional checks cannot change the result.

Restart always restores the same empty 4 by 4 board, the same five clues, a zero score, and no mistakes. The fixed board supports meaningful regression checks: tests verify the Latin-square solution, independently compute every directional clue, prove one solution through permutation backtracking, prove every displayed clue necessary, confirm the harmless incomplete state, exercise both incorrect attempts, verify Restart, and freeze input after either terminal result.

The interface works with pointer, touch, and keyboard input. Every grid cell is a real button with its row, column, and current height in the accessible label. Digit controls meet the site's touch-height convention, and the board uses zero-minimum fractional columns so it stays within a narrow mobile viewport. The selected lot has a visible outline that does not depend on color alone. The shared game shell also provides the site's double-Escape boss key, which temporarily swaps the game for a spreadsheet-style screen and restores the unchanged puzzle when toggled again.

All puzzle state stays in the current browser. The game does not upload the grid, call a puzzle service, request an account, or introduce a new client dependency. If local storage is available, only the best completed score is retained through the existing game shell. The linked sources support the public rules and terminology; they do not supply or endorse this product-authored puzzle.

This is casual entertainment and transparent logic practice, not a standardized intelligence, educational, aptitude, psychological, or clinical assessment. The score records completion of this one deterministic fixture under its stated two-error policy. It should not be used to rank people or make decisions about learning, employment, health, or ability. The related games provide other fixed-grid deduction styles when you want a different local challenge.

Methodology & sources

The released fixture stores one product-authored 4 by 4 Latin-square solution and four directional clue arrays where zero means omitted. A visibility scan starts at zero height and counts only values that exceed the running maximum. Fixture validation requires every row and column to be a permutation of 1 through 4 and every nonzero edge clue to equal the independently calculated scan from its direction. A separate solver generates all 24 row permutations, filters left and right clues, backtracks through column-unique row choices, prunes impossible top-clue prefixes, validates all directions at completion, stops after two solutions, and must count exactly one. Removing each of the five displayed clues must raise the count above one. Runtime checking ignores incomplete submissions, allows one editable incorrect completed check, deadlocks on the second, awards exactly 1,000 for the valid grid, and freezes terminal states.

Frequently asked questions

How is a Skyscrapers edge clue counted?
Scan inward from that clue and count a building only when it is taller than every building already seen. The first building always counts.
Does this fixed puzzle have exactly one solution?
Yes. An independent row-permutation backtracking test counts exactly one solution, and removing any one shown clue produces multiple solutions.
Does checking an incomplete board use a mistake?
No. An incomplete check only shows guidance. The first incorrect completed board remains editable, while a second incorrect completed check deadlocks the run.
Can I play on mobile or entirely by keyboard?
Yes. The compact grid fits a narrow viewport. Arrow keys move, keys 1 through 4 enter heights, Delete clears, and Enter checks the skyline.

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