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Omni-MATH / Fix positive integers k,n. A candy vending machine has many different colours of candy, where there are 2n candies of each colour. A couple of kids each buys from the vending machi…

Problem

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problem

Fix positive integers

k,n

. A candy vending machine has many different colours of candy, where there are

2n

candies of each colour. A couple of kids each buys from the vending machine

2

candies of different colours. Given that for any

k+1

kids there are two kids who have at least one colour of candy in common, find the maximum number of kids.

Plain-text mathematical notation (without MathML)

Fix positive integers k,n. A candy vending machine has many different colours of candy, where there are 2n candies of each colour. A couple of kids each buys from the vending machine 2 candies of different colours. Given that for any k+1 kids there are two kids who have at least one colour of candy in common, find the maximum number of kids.

Original LaTeX notation

Fix positive integers $k,n$. A candy vending machine has many different colours of candy, where there are $2n$ candies of each colour. A couple of kids each buys from the vending machine $2$ candies of different colours. Given that for any $k+1$ kids there are two kids who have at least one colour of candy in common, find the maximum number of kids.

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Source and history

task_id: 1e1ea259-e2f3-5dee-a8a0-9747193bc2de
task_key: test--1e1ea259-e2f3-5dee-a8a0-9747193bc2de
task_revision_id: 2
config / split: / test

Official source

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