Every third step of a staircase with 2023 steps is colored black. The first seven steps are shown in the diagram. Anita walks up the steps one at a time starting with either her right or left foot alternating each step. What is the smallest number of black steps she will step on with her right foot? Notice that we have a very nice pattern on our staircase that repeats every six steps. We have two black stairs in every six steps and each of these black stairs are three steps away from each other. Because they're three steps away from each other she'll step on one with her left foot and the other with her right foot in every group of six steps. Therefore in each of these six step groups she will step on one black step with her right foot. We can show that 2023 equals six times 337 plus one. Therefore because there are 337 groups of six and she steps on exactly one black step with her right foot in each group then she'll step on exactly 337 black steps so our correct answer is D, 337.

staircase

black steps

Anita

right foot

pattern