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Omni-MATH / There are 100 people in a room with ages 1,2,…,100. A pair of people is called cute if each of them is at least seven years older than half the age of the other person in the pair.…

Problem

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problem

There are 100 people in a room with ages 1,2,…,1001,2, \ldots, 100. A pair of people is called cute if each of them is at least seven years older than half the age of the other person in the pair. At most how many pairwise disjoint cute pairs can be formed in this room?
Plain-text mathematical notation (without MathML)
There are 100 people in a room with ages 1,2,…,100. A pair of people is called cute if each of them is at least seven years older than half the age of the other person in the pair. At most how many pairwise disjoint cute pairs can be formed in this room?
Original LaTeX notation
There are 100 people in a room with ages $1,2, \ldots, 100$. A pair of people is called cute if each of them is at least seven years older than half the age of the other person in the pair. At most how many pairwise disjoint cute pairs can be formed in this room?

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Source and history

task_id
e3d19162-df50-5c45-b762-fe0c8ec8e29f
task_key
test--e3d19162-df50-5c45-b762-fe0c8ec8e29f
task_revision_id
1
config / split
/ test

Official source

initial import