HW 2025-03-07 AO

[CMFMS 2.511]

How many distinct triangles can be traced along the lines in the diagram below?

[CMFMS 2.611]

John walks six blocks on a city grid of sidewalks to his favorite deli for lunch: three blocks north and three blocks west. He never uses the exact same path on his return to work. If John always stays on city sidewalks and goes six blocks each way, how many different ways can John walk to the deli and back?

[CMFMS 2.711]

Twelve points are arranged into six rows of four points each in the shape of a six-pointed star. How many ways can three of these points be connected to form a triangle?

[CMFMS 2.811]

How many pentagons can be formed by tracing the lines of the figure below?

[CMFMS 2.911]

A regular dodecahedron has 12 pentagonal faces, 20 vertices, and 30 edges. How many of the triangles which can be formed by connecting three of its vertices have at least one side within the dodecahedron?

[CMFMS 2.021]

How many two-digit integers use two different digits?

[CMFMS 2.121]

There are seven parking spaces in a row which must be assigned to four co-workers. How many ways can the spaces be assigned if at least two of the assigned spaces must be adjacent?

[CMFMS 2.221]

How many different ways can six friends stand in line at the movies if Alice and David refuse to stand next to each other?

[CMFMS 2.321]

How many positive integers less than 50 are not divisible by 3 or 5?

[CMFMS 2.421]

A fair coin is flipped ten times. How many ways are there to flip more heads than tails?