Number Theory
Rainbow Cycles
If all integers are colored in the same pattern as the numbers in this grid, what color is 1234?
Rainbow Cycles
Modular arithmetic is the part of number theory used to study cyclical systems: systems where taking enough steps “forward” brings you back to where you started. In this quiz we'll focus exclusively on abstract coloring patterns so that we can find some general shortcuts for working with these systems.
In the modular arithmetic units later in this course, we'll expand these theories and more into shortcuts that can be applied to many real-life modular systems:
Rainbow Cycles
If you multiply a blue number by an orange number, what color will the product be?
Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.
Rainbow Cycles
If you add a blue number (like 2 or 7) to a yellow number (like 4 or 9), what color will the sum be?
Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.
Rainbow Cycles
If you multiply a green number by a yellow number, what color will the product be?
Note: Assume that all integers are colored according to the same pattern as the numbers in the grid.
Rainbow Cycles
What color is
Note: Assume that all integers are colored according to the same pattern (blue, then green, then orange) as the numbers in the grid.