MathDB

5

Part of 2016 AIME Problems

Problems(2)

Anh read a book

Source: 2016 AIME I #5

3/4/2016
Anh read a book. On the first day she read nn pages in tt minutes, where nn and tt are positive integers. On the second day Anh read n+1n + 1 pages in t+1t + 1 minutes. Each day thereafter Anh read one more page than she read on the previous day, and it took her one more minute than on the previous day until she completely read the 374374 page book. It took her a total of 319319 minutes to read the book. Find n+tn + t.
2016 AIME IAIME
Bermuda Triangle

Source: 2016 AIME II #5

3/17/2016
Triangle ABC0ABC_0 has a right angle at C0C_0. Its side lengths are pairwise relatively prime positive integers, and its perimeter is pp. Let C1C_1 be the foot of the altitude to AB‾\overline{AB}, and for n≥2n\geq 2, let CnC_n be the foot of the altitude to Cn−2B‾\overline{C_{n-2}B} in △Cn−2Cn−1B\triangle C_{n-2}C_{n-1}B. The sum ∑n=1∞Cn−1Cn=6p\sum\limits_{n=1}^{\infty}C_{n-1}C_n = 6p. Find pp.
AMCAIMEAIME II2016 AIME II2016 AIME II Problem 5geometryright triangle