Problem
ALG-B1-M12-P022 Variant 6, Problem 2
#22
★★★★☆ Level 4 of 5
\(P\) has degree at most \(3\), values \(1,2,5,10\) at \(0,1,2,3\). Find \(P(4)\).
Third differences are constant.
Differences: \(1,3,5\); second differences \(2,2\); next first difference \(7\). Answer \(17\).
Mock olympiad problem. Tags: finite-differences.