Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 2000 based on Logarithms and Equations. Logarithms and Equations – AIME I 2000 \(log_{10}(2000xy)-log_{10}xlog_{10}y=4\) and \(log_{10}(2yz)-(log_{10}y)(log_{10}z)=1\) and...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations. Theory of Equations – AIME I, 2015 The expressions A=\(1\times2+3\times4+5\times6+…+37\times38+39\)and...

Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 1999 based on Probability in games. Probability in Games – AIME I, 1999 Question 13 Forty teams play a tournament in which every team plays every other team exactly once. No...

Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on Probability of tossing a coin. Probability of tossing a coin – AIME I, 2009 Question 3 A coin that comes up heads with probability p>0and tails with...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2009 based on Equations with a number of variables. Equations with number of variables – AIME 2009 For t=1,2,3,4, define \(S^{t}=a^{t}_1+a^{t}_2+…+a^{t}_{350}\), where...

Try this beautiful problem from American Invitational Mathematics Examination I, AIME I, 2009 based on geometric sequence. Geometric Sequence Problem – AIME 2009 Call a 3-digit number geometric if it has 3 distinct digits which, when read from left to right,...