Nonogram: Play here: https://www.puzzle-nonograms.com/
Math Exploration
Scenario: Suppose you have one or more rectangular blocks of different lengths to fit inside one long array of a fixed length. If those blocks must have at least one unit of space between them, how many different ways can they fit into the long block?
Suppose you have two unit blocks that you can place into a row of five blocks. There must be at least one unit of space between them. How many ways can you do so?
Let x represent a block and 0 a space. Here are two possible configurations:
x0x00
x000x
How many ways can you do this? Can you find the others?
What if you have one block? What's the maximum number of blocks you can have?
What if you have a block of length 2 and a block of length 1? e.g. 0xx0x
To give some notation, let's call the long array N (its size) and the list the number and length of blocks in a list called hint.
N=5, hint=[1,1]
N=5, hint=[1]
N=5, hint=[2,1]
What if you increase the length of the array to six and seven units, i.e. N=6, 7? You can get more blocks the longer your array gets, e.g. hint=[1,2,1].
MAA Section Meeting at Belhaven University, Jackson, MS
https://www.la-ms.maa.org/meeting2025
Contact Dr. Talley or Dr. Wright if you are interesting in attending, and indicate whether you would like to participate in the Integration Bee.