Problems(6)
1999 Advanced Topics #2: Stacy Goes Shopping
Source:
6/21/2012
Stacy has dollars. She enters a mall with shops and a lottery stall. First she goes to the lottery and her money is doubled, then she goes into the first shop and spends dollars. After that she alternates playing the lottery and getting her money doubled (Stacy always wins) then going into a new shop and spending . When she comes out of the last shop she has no money left. What is the minimum possible value of ?
1999 Algebra #2: Positive Integer That Divides Into 91
Source:
6/21/2012
For what single digit does divide the -digit number ?
modular arithmetic
1999 Calculus #2: Sides of a Rectangle
Source:
6/21/2012
A rectangle has sides of length and for some . What is the largest possible area of such a rectangle?
calculusgeometryrectangletrigonometry
1999 HMMT Geometry # 2
Source:
3/3/2024
A semicircle is inscribed in a semicircle of radius as shown. Find the radius of the smaller semicircle.
https://cdn.artofproblemsolving.com/attachments/c/1/c60cd40eaecfe417aca46ce4fd386fe22af85b.png
geometry
a ladder is leaning against a house 1999 HMMT Team 2
Source:
1/1/2022
A ladder is leaning against a house with its lower end feet from the house. When the lower end is pulled feet farther from the house, the upper end slides feet down. How long is the ladder (in feet)?
geometryright triangle
1999 Oral #2: Allergic Reactions
Source:
10/20/2012
Alex, Pei-Hsin, and Edward got together before the contest to send a mailing to all the invited schools. Pei-Hsin usually just stu ffs the envelopes, but if Alex leaves the room she has to lick them as well and has a chance of dying from an allergic reaction before he gets back. Licking the glue makes Edward a bit psychotic, so if Alex leaves the room there is a chance that Edward will kill Pei-Hsin before she can start licking envelopes. Alex leaves the room and comes back to fi nd Pei-Hsin dead. What is the probability that Edward was responsible?
probability