Cool Skyscrapers Puzzle - Cut-the-Knot

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Discussion Overview

The discussion revolves around a puzzle inspired by skyscrapers, exploring its structure and potential variations. Participants share insights on strategies for solving the puzzle, including comparisons to Sudoku and observations on visibility constraints.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant suggests modifying the puzzle to resemble a Sudoku format, incorporating a 9x9 Latin square with 3x3 subsquares and visibility constraints.
  • Another participant notes that having the edge numbers as either 1 or n simplifies the puzzle, leading to a unique solution.
  • A different participant claims that if the sum of the numbers at the ends of a row or column equals n+1, it aids in determining the placement of n within that row/column.
  • One participant shares their success in solving an 8x8 puzzle, mentioning the need for some guessing.

Areas of Agreement / Disagreement

Participants express individual strategies and observations, but there is no consensus on a single approach or solution method. Multiple viewpoints and techniques are presented without resolution.

Contextual Notes

Some strategies depend on specific configurations of the puzzle, and the effectiveness of proposed methods may vary based on the puzzle size and complexity.

Who May Find This Useful

Individuals interested in puzzle-solving, particularly those who enjoy logic puzzles and combinatorial games.

fourier jr
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http://www.cut-the-knot.org/Curriculum/Games/Skyscrapers.shtml

I wonder of they could make it more like sudoku where there's a 9x9 latin square made out of 3x3 subsquares where only certain numbers of skyscrapers are visible in each rown & column of each subsquare. & beware the creepy eyes watching your every move. Anyway I've found that it's easier when the numbers on the edge are either 1 or n for an nxn, which means there's only one possibility.
 
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Nice one.
 
I think I've also found that if the sum of the numbers on either end of a row or column is n+1 then it's easy to figure out where n goes in that row/column. It takes some practice. I'm still trying to get through the 7x7 square
 
Last edited:
woohoo just solved my first 8x8, & I only had to guess twice :biggrin:
 

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