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For a Traveling Salesman Problem instance with 304 cities, there are approximately $2.3 x 10^624$ possible unique routes. This number is derived from the factorial growth of permutations, specifically (304-1)! / 2, accounting for the fact that the starting city and direction do not matter for undirected cycles.

Conditions: The problem has 304 distinct cities.; Routes are considered as unique Hamiltonian cycles (direction and starting point do not matter).

For a Traveling Salesman Problem instance with 304 cities, there are approximately $2.3 x 10^624$ possible unique routes. This number is derived from the factorial growth of permutations, specifically (304-1)! / 2, accounting for the fact that the starting city and direction do not matter for undirected cycles.

Conditions: The problem has 304 distinct cities.; Routes are considered as unique Hamiltonian cycles (direction and starting point do not matter).

To relate prototype and model behavior, the lecture matches each dimensionless group in the prototype expression to the corresponding group in the model expression. The equalities for $\Pi_2, \ldots, \Pi_{N-1}$ are the similarity requirements, and the first equality $\Pi_1^{(p)} = \Pi_1^{(m)}$ is the prediction equation.

Conditions: Applied to the prototype-model pair written on the board.; The method separates the first group, used for prediction, from the remaining groups, used as similarity requirements.; The underlying physics governing the flow must be identical for both the prototype and the model.

To relate prototype and model behavior, the lecture matches each dimensionless group in the prototype expression to the corresponding group in the model expression. The equalities for $\Pi_2, \ldots, \Pi_{N-1}$ are the similarity requirements, and the first equality $\Pi_1^{(p)} = \Pi_1^{(m)}$ is the prediction equation.

Conditions: Applied to the prototype-model pair written on the board.; The method separates the first group, used for prediction, from the remaining groups, used as similarity requirements.; The underlying physics governing the flow must be identical for both the prototype and the model.