Algebra Fundamentals


In this quiz we explore various sequences, which not only make for fun puzzles but are central to algebra.

Could you describe this pattern well enough that someone could reproduce it without having seen it?


How many squares will be in Step 99?


Does column 15 have more stars or squares?

Hint: notice that each horizontal row has its own pattern.


In each figure, squares are either empty or filled with a circle. How many empty squares does Figure 10 have?


Unit cubes are stacked to create a large cube and then painted green. If we stack a bunch of unpainted cubes into a larger \(10 \times 10 \times 10\) cube then painted the outside, how many of the small unit cubes will have exactly one face painted green?


Jill is arranging tables for party that will be placed in one long row, end to end. Each side of each table can seat one person.

Which table shape cannot seat exactly 50 people, regardless of the number of tables used?


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