This cute little problem gives us the wisdom that when we minimize two functions at single point uniquely , then their sum is also minimized at the same point. This is applied to calculate the least square estimates of two group regression from ISI MStat 2016 Problem 7.
This problem from ISI MStat 2016 is an application of the ideas of indicator and independent variables and covariance of two summative random variables.
This ISI MStat 2016 problem is an application of the ideas of tracing the trace and Eigen values of a matrix and using a cute sum of squares identity.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Planes and distance.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1985 based on GCD and Sequence.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Equations and roots. You may use sequential hints.
Try this beautiful problem from the Pre-RMO, 2017 based on GCD and Primes. You may use sequential hints to solve the problem.
Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Integer and Divisibility. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1984 based on Function and symmetry. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2008 based on Logic and speed.