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 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...

Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2011 based on Permutation. Permutation Problem (SMO Entrance) A \(4 \times 4\) Sudoku grid is filled with digits so that each column , each row and each of the four \( 2 \times 2\) sub grids that...

Try this problem from the Singapore Mathematics Olympiad, SMO, 2010 based on the application of the Pythagoras Theorem. Application of Pythagoras Theorem- (SMO Test) The figure below shows a circle with diameter AB. C ad D are points on the circle on the same side of...

Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. Problem – Functional equations (SMO Test) Let L denote the minimum value of the quotient of a 3- digit number formed by three distinct divided by the sum of its...