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Problems
Contests
National and Regional Contests
Iran Contests
Iran Team Selection Test
2024 Iran Team Selection Test
11
11
Part of
2024 Iran Team Selection Test
Problems
(1)
Sepehr the chemist
Source: Iran Team selection test 2024 - P11
5/19/2024
Let
n
<
k
n<k
n
<
k
be two natural numbers and suppose that Sepehr has
n
n
n
chemical elements ,
2
k
2k
2
k
grams from each , divided arbitrarily in
2
k
2k
2
k
cups.Find the smallest number
b
b
b
such that there is always possible for Sepehr to choose
b
b
b
cups , containing at least
2
2
2
grams from each element in total.Proposed by Josef Tkadlec & Morteza Saghafian
combinatorics