House Numbers Math Puzzle

Abe, Buddy, Carmen, Dennis and Earl all live on Pine Street which has house numbers from 10 to 111, inclusive. Two of them live in the same house. The others all live in different houses. They all have made remarks about where they live, but not all the remarks are true.

Abe said, "My house number is a factor of Buddy's house number. Earl's house number is 10 greater than Dennis'."

Buddy said, "My house number is greater than 70. Abe's house number is greater than 30."

Carmen said, "My house number is both a cube and a square. Dennis's house number is greater than 50."

Dennis said, "My house number is a square. Buddy's house number is a cube."

Earl said, "My house number is twice Buddy's"

But who's telling the truth? It turns out that all statements made by people living in houses with numbers greater than 50 were false. All the other statements were true.

Can you match the names with the house numbers?

Adapted from Brain Puzzlers Delight by E.R. Emmet

Click to find the answer to this math puzzle.