Subcontests
(6)What are those points?
Let ABC be an isosceles triangle with AB=AC. Suppose P,Q,R are points on segments AC,AB,BC respectively such that AP=QB, ∠PBC=90∘−∠BAC and RP=RQ. Let O1,O2 be the circumcenters of △APQ and △CRP. Prove that BR=O1O2.Proposed by Atul Shatavart Nadig K-pop sequences
Let k be a positive integer. A sequence of integers a1,a2,⋯ is called k-pop if the following holds: for every n∈N, an is equal to the number of distinct elements in the set {a1,⋯,an+k}. Determine, as a function of k, how many k-pop sequences there are.Proposed by Sutanay Bhattacharya