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Portugal MO
2006 Portugal MO
6
6
Part of
2006 Portugal MO
Problems
(1)
no numbers in 6 chosen from a total of 36 numbers
Source: Portugal OPM 2006 p6
5/19/2024
Integers
1
1
1
to
36
36
36
are written in each "Neuro-Millions" bulletin. A bet on "Neuro-Millions" consists of choosing
6
6
6
of these
36
36
36
numbers. Then,
6
6
6
numbers between
1
1
1
and
36
36
36
are drawn, and these constitute the key to "Neuro-Milh˜oes". A bet is awarded if it does not contain any of the key numbers. How many bets, at least, are necessary to guarantee a prize?
combinatorics