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MathNet 2024-part-03 — 168 problems (EN–VI) Question 36

Math Olympiad Vault · MathNet 2024-part-03 — 168 problems (EN–VI)

Question 36

There are $2n$ beakers and $k \lt n$ chemical substances. In these beakers we have, in aggregate, $2n$ grams of each substance, and the weight of every substance in each beaker is a non-negative real number. Find the smallest value of $s$ such that we can always find $s$ beaker(s) that in aggregate contain at least $2$ grams of each substance.