HMMT 2013 T2
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A cafe has 3 tables and 5 individual counter seats. People enter in groups of size between 1 and 4 , inclusive, and groups never share a table. A group of more than 1 will always try to sit at a table, but will sit in counter seats if no tables are available. Conversely, a group of 1 will always try to sit at the counter first. One morning, groups consisting of a total of people enter and sit down. Then, a single person walks in, and realizes that all the tables and counter seats are occupied by some person or group. What is the minimum possible value of ?
Dataset text NuminaMath olympiads. Quoted with source.
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