Problem Set Workbook
Access the downloadable workbook for 2015 USAJMO Day 2 problems here.
Discussion Forum
Engage in discussion about the 2015 USAJMO Day 2 math contest by visiting Random Math USAJMO Day 2 2015 Forum
Individual Problems and Solutions
For problems and detailed solutions to each of the 2015 USAJMO Day 2 problems, please refer below:
Problem 4: Find all functions such that
for all rational numbers that form an arithmetic progression. ( is the set of all rational numbers.)
Solution:
Problem 5: Let be a cyclic quadrilateral. Prove that there exists a point on segment such that and if and only if there exists a point on segment such that and .
Solution:
Problem 6: Steve is piling indistinguishable stones on the squares of an grid. Each square can have an arbitrarily high pile of stones. After he is finished piling his stones in some manner, he can then perform stone moves, defined as follows. Consider any four grid squares, which are corners of a rectangle, i.e. in positions for some , such that and . A stone move consists of either removing one stone from each of and and moving them to and respectively, or removing one stone from each of and and moving them to and respectively.
Two ways of piling the stones are equivalent if they can be obtained from one another by a sequence of stone moves.
How many different non-equivalent ways can Steve pile the stones on the grid?
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions