MathDB

1

Part of 2019 AIME Problems

Problems(2)

Sum of digits

Source: 2019 AIME I #1

3/14/2019
Consider the integer N=9+99+999+9999+⋯+99…99⏟321 digits.N = 9 + 99 + 999 + 9999 + \cdots + \underbrace{99\ldots 99}_\text{321 digits}. Find the sum of the digits of NN.
AMCAIMEAIME I2019 AMC2019 AIME I
Two Congruent Triangles

Source: 2019 AIME II #1

3/22/2019
Points C≠DC\neq D lie on the same side of line ABAB so that △ABC\triangle ABC and △BAD\triangle BAD are congruent with AB=9AB = 9, BC=AD=10BC=AD=10, and CA=DB=17CA=DB=17. The intersection of these two triangular regions has area mn\tfrac mn, where mm and nn are relatively prime positive integers. Find m+nm+n.
AMCAIMEAIME IIgeometrycongruent triangles2019 AIME II2019 AMC