Math Problem Statement
A frog is travelling from point A(0, 0) to point B(5,6) but each step can only be 1 unit up or 1 unit to the right. Additionally, the frog refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.
Solution
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Math Problem Analysis
Mathematical Concepts
Combinatorics
Dynamic Programming
Pathfinding
Formulas
Binomial Coefficient: C(n, k) = n! / (k!(n-k)!)
Recurrence Relation: f(m, n) = f(m-1, n) + f(m, n-1)
Theorems
Binomial Theorem
Dynamic Programming Principle
Suitable Grade Level
Grades 10-12
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