Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Number of points and planes. Number of points and planes – AIME I, 1999 Ten points in the plane are given with no three collinear. Four distinct segments...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Sequence and fraction. Sequence and fraction – AIME I, 2000 A sequence of numbers \(x_1,x_2,….,x_{100}\) has the property that, for every integer k...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME I, 1996 based on Finding the smallest positive Integer. Finding smallest positive Integer – AIME I, 1996 Find the smallest positive integer solution to...

Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 1996 based on Roots of Equation and Vieta’s formula. Roots of Equation and Vieta’s formula – AIME I, 1996 Suppose that the roots of \(x^{3}+3x^{2}+4x-11=0\) are...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Tetrahedron. Tetrahedron Problem – AIME I, 1992 Faces ABC and BCD of tetrahedron ABCD meet at an angle of 30,The area of face ABC=120, the area of face BCD...

Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Triangle and integers. Triangle and integers – AIME I, 1995 Triangle ABC is isosceles, with AB=AC and altitude AM=11, suppose that there is a point D on AM...