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

2024 Israel TST, P2
Tags: function , averages , Trees , combinatorics
A positive integer $N$ is given. Panda builds a tree on $N$ vertices, and writes a real number on each vertex, so that $1$ plus the number written on each vertex is greater or equal to the average of the numbers written on the neighboring vertices. Let the maximum number written be $M$ and the minimal number written $m$. Mink then gives Panda $M-m$ kilograms of bamboo. What is the maximum amount of bamboo Panda can get?

2014 JHMMC 7 Contest, 11
Tags: averages , JHMMC , arithmetic mean
What number is exactly halfway between $\frac 1 6$ and $\frac 1 4$?