Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and greatest integer. Sequence and greatest integer – AIME I, 2000 Let S be the sum of all numbers of the form \(\frac{a}{b}\),where a and b are...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Inscribed circle and perimeter. Inscribed circle and perimeter – AIME I, 1999 The inscribed circle of triangle ABC is tangent to AB at P, and its radius is...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Series and sum. Series and sum – AIME I, 1999 given that \(\displaystyle\sum_{k=1}^{35}sin5k=tan\frac{m}{n}\) where angles are measured in degrees, m and n...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1998 based on LCM and Integers. Lcm and Integer – AIME I, 1998 Find the number of values of k in \(12^{12}\) the lcm of the positive integers \(6^{6}\), \(8^{8}\) and k. is...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996 based on Greatest Positive Integer. Positive Integer – AIME I, 1996 For each real number x, Let [x] denote the greatest integer that does not exceed x,find number of...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1993 based on Integers. Integer – AIME I, 1993 Find the number of four topics of integers (a,b,c,d) with 0<a<b<c<d<500 satisfy a+d=b+c and bc-ad=93. is...