On Determining Paint by Numbers Puzzles with Nonunique Solutions
Sacred Heart University
Fairfield, CT 06825
Paint by Numbers is a classic logic puzzle in which the squares of a
p × n
grid are to be colored in such a way as to display a picture.
The decision on which squares to color is determined by sequences of
numbers above each column and to the left of each row. The numbers
describe how many consecutive squares are to be colored in that row or
column, and multiple numbers represent multiple blocks of colored in
squares (with at least one uncolored square inbetween blocks). Certain
natural questions arise. For a given p × n grid, how many
possible sequences are in a single column or row? For a given grid,
how many puzzles are there? How many of these have unique solutions?
We will explore these questions as well as connections between Paint by
Numbers puzzles, partition theory, and the Fibonacci sequence.
Full version: pdf,
(Concerned with sequences
Received July 9 2009;
revised version received August 31 2009.
Published in Journal of Integer Sequences, September 1 2009.
Journal of Integer Sequences home page