MathDB

6

Part of 2001 AIME Problems

Problems(2)

Rolling Die

Source:

12/6/2005
A fair die is rolled four times. The probability that each of the final three rolls is at least as large as the roll preceding it may be expressed in the form m/n,m/n, where mm and nn are relatively prime positive integers. Find m+n.m+n.
probabilityAMCAIMEanalytic geometrycountingdistinguishabilitynumber theory
Squares in Circles

Source:

12/28/2006
Square ABCDABCD is inscribed in a circle. Square EFGHEFGH has vertices EE and FF on CD‾\overline{CD} and vertices GG and HH on the circle. The ratio of the area of square EFGHEFGH to the area of square ABCDABCD can be expressed as mn\frac{m}{n} where mm and nn are relatively prime positive integers and m<nm<n. Find 10n+m10n+m.
ratiogeometrynumber theoryrelatively primePythagorean Theorempower of a point