MathDB

4

Part of 2014 ASDAN Math Tournament

Problems(5)

2014 Algebra #4

Source:

7/8/2022
Let f(x)=∑i=12014∣x−i∣f(x)=\sum_{i=1}^{2014}|x-i|. Compute the length of the longest interval [a,b][a,b] such that f(x)f(x) is constant on that interval.
2014Algebra Test
2014 Advanced #4

Source:

7/1/2022
Cynthia and Lynnelle are collaborating on a problem set. Over a 2424-hour period, Cynthia and Lynnelle each independently pick a random, contiguous 66-hour interval to work on the problem set. Compute the probability that Cynthia and Lynnelle work on the problem set during completely disjoint intervals of time.
2014Advanced Topics Test
2014 General #4

Source:

7/4/2022
If Bobby’s age is increased by 66, it’s a number with an integral (positive) square root. If his age is decreased by 66, it’s that square root. How old is Bobby?
2014General Test
2014 Team #4

Source:

7/1/2022
A frog is hopping from (0,0)(0,0) to (8,8)(8,8). The frog can hop from (x,y)(x,y) to either (x+1,y)(x+1,y) or (x,y+1)(x,y+1). The frog is only allowed to hop to point (x,y)(x,y) if ∣y−x∣≤1|y-x|\leq1. Compute the number of distinct valid paths the frog can take.
2014team test
2014 Geometry #4

Source:

7/12/2022
Consider a square ABCDABCD with side length 44 and label the midpoint of side BCBC as MM. Let XX be the point along AMAM obtained by dropping a perpendicular from DD onto AMAM. Compute the product of the lengths XCXC and MDMD.
2014Geometry Test