Question 34
A set of identical square tiles with side length $1$ is placed on a (very large) floor. Every tile after the first shares an entire edge with at least one tile that has already been placed.
- What is the largest possible perimeter for a figure made of $10$ tiles?
- What is the smallest possible perimeter for a figure made of $10$ tiles?
- What is the largest possible perimeter for a figure made of $2011$ tiles?
- What is the smallest possible perimeter for a figure made of $2011$ tiles?
Prove that your answers are correct.
- What is the largest possible perimeter for a figure made of $10$ tiles?
- What is the smallest possible perimeter for a figure made of $10$ tiles?
- What is the largest possible perimeter for a figure made of $2011$ tiles?
- What is the smallest possible perimeter for a figure made of $2011$ tiles?
Prove that your answers are correct.