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Omni-MATH / 101 people, sitting at a round table in any order, had 1,2,...,101 cards, respectively. A transfer is someone give one card to one of the two people adjacent to him. Find the small…

Problem

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problem

101

people, sitting at a round table in any order, had

1,2,... , 101

cards, respectively. A transfer is someone give one card to one of the two people adjacent to him. Find the smallest positive integer

k

such that there always can through no more than

k

times transfer, each person hold cards of the same number, regardless of the sitting order.

Plain-text mathematical notation (without MathML)

101 people,  sitting at a round table in any order,  had  1,2,...,101 cards,  respectively.  
A transfer is someone give  one  card  to one of  the two people  adjacent to him.
Find the  smallest positive integer k such that   there always  can  through  no more than  k  times transfer,  each person  hold cards of the same number, regardless of  the sitting order.

Original LaTeX notation

$101$ people,  sitting at a round table in any order,  had  $1,2,... , 101$ cards,  respectively.  
A transfer is someone give  one  card  to one of  the two people  adjacent to him.
Find the  smallest positive integer $k$ such that   there always  can  through  no more than  $ k $  times transfer,  each person  hold cards of the same number, regardless of  the sitting order.

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task_id: 1d3f97a3-fb71-58d0-a690-9d7b6a44bc90
task_key: test--1d3f97a3-fb71-58d0-a690-9d7b6a44bc90
task_revision_id: 2
config / split: / test

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