Try to solve this problem number 35 from Singapore Mathematics Olympiad, SMO, 2018 based on Functional Equation. Problem – Functional Equation (SMO Entrance) Consider integers \({1,2, \ldots, 10}\). A particle is initially -at 1 . It moves to an adjacent integer...

Try this beautiful Logarithm Problem From Singapore Mathematics Olympiad, SMO, 2011 (Problem 7). Logarithm Problem From SMO Let \(x=\frac {1}{\log_{\frac {1}{3}} \frac {1}{2}}\)+\(\frac {1}{\log_{\frac {1}{5}} \frac {1}{4}}\)+\(\frac {1}{\log _{\frac {1}{7}}...

Try this beautiful problem from Singapore Mathematical Olympiad, SMO, 2010 – Problem 7 based on the combination of equations. Problem – Combination of Equations (SMO Entrance) Find the sum of all the positive integers p such that the expression (x-p) (x...

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2009 based on Trigonometry Simplification. Problem – Trigonometry Simplification (SMO Entrance) If \(\frac {cos 100^\circ}{1-4 sin 25^\circ cos 25^\circ cos 50^\circ} = tan x^\circ \) Find \(...

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2012 based on Probability. Problem – Probability (SMO Entrance) Two players A and B play rock – paper – scissors continuously until player A wins 2 consecutive games. Suppose each...