This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2020 Hong Kong TST, 4
Tags: algebra , hong kong tst , fe , real , functional equation
Find all real-valued functions $f$ defined on the set of real numbers such that $$f(f(x)+y)+f(x+f(y))=2f(xf(y))$$ for any real numbers $x$ and $y$.

2023 Hong Kong Team Selection Test, Problem 1
Tags: hong kong tst
Mandy needs to wake up early for attending a mathematics contest. She has set an alarm in her smartphone every 15 minutes since 5:30 am. If an alarm is not pressed off by her or her mother (or anything else), it will ring for a while, stop for a while, then will ring again 9 minutes later as the first ring, and so on (e.g. if the first alarm is not pressed off, it will ring again at 5:39 am). Also each alarm will work independently. Now suppose each ring-tone lasts for $x$ minutes, and the smartphone has eventually rung for 50 minutes before Mandy wakes up at 6:30 am (assume no one has pressed off any alarm before that). Find the value of $x$.