MathDB

17

Part of 2016 Purple Comet Problems

Problems(2)

Purple Comet 2016 HS Problem 17

Source:

4/12/2018
The cubic polynomials p(x)p(x) and q(x)q(x) satisfy • p(1)=q(2)p(1) = q(2) • p(3)=q(4)p(3) = q(4) • p(5)=q(6)p(5) = q(6) • p(7)=q(8)+13p(7) = q(8) + 13. Find p(9)−q(10)p(9)-q(10).
Purple Comet
Purple Comet 2016 MS Problem 17

Source:

4/13/2018
Suzie flips a fair coin 6 times. The probability that Suzie flips 3 heads in a row but not 4 heads in a row is given by mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm + n.
Purple Comet