Please reason step by step, and put your final answer within \boxed{}.
Petya bought a "Constructor" set that contains 100 sticks of different lengths. The instructions for the "Constructor" state that any three sticks from the set can form a triangle. Petya decided to test this claim by trying to form triangles from the sticks. The sticks are sorted in ascending order of length. What is the minimum number of checks (in the worst-case scenario) Petya needs to make to prove or disprove the instruction's claim?
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