#### Euler's formula

The Euler's formula states that for any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. This can be proven using the Noah's Ark method, which states that if you have a convex polyhedron with V vertices, E edges, and F faces, then V - E + F = 2.

#### Problem

`Prove and explain the proof of the Euler's formula, using Noah's Ark method. For any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically: V - E + F = 2. For instance, a tetrahedron has four vertices, four faces, and six edges: 4 - 6 + 4 = 2.`

#### Solution

`The Euler's formula can be proved by the Noah's Ark method. For any convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges. Symbolically: V - E + F = 2. For instance, a tetrahedron has four vertices, four faces, and six edges: 4 - 6 + 4 = 2.`

A.I. Evaluation of the Solution

The candidate's solution correctly states the Euler's formula and provides a valid proof by the Noah's Ark method. However, the solution could be more complete by providing more explanation and examples. For instance, the candidate could explain how the Noah's Ark method works and provide additional examples to illustrate the proof.

Evaluated at: 2022-11-11 03:38:23