On the number of forceless hint sequences in paint-by-numbers puzzles

D. Berend; S. Zucker

On the number of forceless hint sequences in paint-by-numbers puzzles

Department of Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

In this paper we consider a question raised in [4] regarding Paint-by-Numbers puzzles. Paint-by-Numbers is a classic logic puzzle in which the squares of a p × n grid are to be colored black or white, according to hints, consisting of the length of the blocks of consecutive black squares in each row and column. Mullen [4] studied the asymptotic probability that a random hint sequence of a row will determine uniquely the color of at least some of the squares in a row, and was able to give lower and upper bounds on this probability. In this paper we tighten his bounds.

Original language	English
Pages	266-269
Number of pages	4
State	Published - 1 Jan 2016
Event	28th Canadian Conference on Computational Geometry, CCCG 2016 - Vancouver, Canada Duration: 3 Aug 2016 → 5 Aug 2016

Conference

Conference	28th Canadian Conference on Computational Geometry, CCCG 2016
Country/Territory	Canada
City	Vancouver
Period	3/08/16 → 5/08/16

ASJC Scopus subject areas

Computational Mathematics
Geometry and Topology

Cite this

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title = "On the number of forceless hint sequences in paint-by-numbers puzzles",

abstract = "In this paper we consider a question raised in [4] regarding Paint-by-Numbers puzzles. Paint-by-Numbers is a classic logic puzzle in which the squares of a p × n grid are to be colored black or white, according to hints, consisting of the length of the blocks of consecutive black squares in each row and column. Mullen [4] studied the asymptotic probability that a random hint sequence of a row will determine uniquely the color of at least some of the squares in a row, and was able to give lower and upper bounds on this probability. In this paper we tighten his bounds.",

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AB - In this paper we consider a question raised in [4] regarding Paint-by-Numbers puzzles. Paint-by-Numbers is a classic logic puzzle in which the squares of a p × n grid are to be colored black or white, according to hints, consisting of the length of the blocks of consecutive black squares in each row and column. Mullen [4] studied the asymptotic probability that a random hint sequence of a row will determine uniquely the color of at least some of the squares in a row, and was able to give lower and upper bounds on this probability. In this paper we tighten his bounds.

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M3 - Paper

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T2 - 28th Canadian Conference on Computational Geometry, CCCG 2016

Y2 - 3 August 2016 through 5 August 2016

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On the number of forceless hint sequences in paint-by-numbers puzzles

Abstract

Conference

ASJC Scopus subject areas

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