MathCounts 2025 Chapter — Sprint Round (Problem 27)Let 2n2^n2n be the greatest power of 2 that divides 1×2×3×4+2×3×4×5+3×4×5×6+⋯+25×26×27×281\times2\times3\times4 + 2\times3\times4\times5 + 3\times4\times5\times6 + \cdots + 25\times26\times27\times281×2×3×4+2×3×4×5+3×4×5×6+⋯+25×26×27×28. What is the value of nnn?Related TopicsToolkit 16 — Hockey Stick IdentityHints (2)Hint 1a(a+1)(a+2)(a+3)=4!(a+34)a(a+1)(a+2)(a+3) = 4!\binom{a+3}{4}a(a+1)(a+2)(a+3)=4!(4a+3)Hint 2Use Identity 16. Hockey Stick Identity.Final Answer333