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This problem is a beautiful application of the probability theory and cauchy functional equation. This is from ISI MStat 2019 PSB problem 4.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on GCD and Ordered pair.

Try this problem from ISI MSQMS 2018 which involves the concept of Inequality. You can use the sequential hints provided to solve the problem.

Try this beautiful problem from the Pre-RMO, 2017 based on Integers and Inequality. You may use sequential hints to solve the problem.

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2011 based on Permutation. You may use sequential hints to solve the problem.

Try this beautiful problem from AMC-10A, 2009 based on Diamond Pattern. You may use sequential hints to solve the problem.

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Problem on Digits. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.

Try this beautiful problem from the Pre-RMO, 2017 based on Series Problem. You may use sequential hints to solve the problem.

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Trigonometry and greatest integer.