Difference between revisions of "2020 IMO Problems/Problem 3"

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Problem 3. There are 4n pebbles of weights 1, 2, 3, . . . , 4n. Each pebble is coloured in one of n
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== Problem ==
colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two
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There are <math>4n</math> pebbles of weights <math>1, 2, 3, . . . , 4n</math>. Each pebble is colored in one of <math>n</math> colors and there are four pebbles of each color. Show that we can arrange the pebbles into two piles so that the following two conditions are both satisfied:
piles so that the following two conditions are both satisfied:
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* The total weights of both piles are the same.
The total weights of both piles are the same.
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* Each pile contains two pebbles of each color.
Each pile contains two pebbles of each colour.
 
  
 
== Video solution ==
 
== Video solution ==
  
 
https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems]
 
https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems]

Revision as of 11:25, 14 May 2021

Problem

There are $4n$ pebbles of weights $1, 2, 3, . . . , 4n$. Each pebble is colored in one of $n$ colors and there are four pebbles of each color. Show that we can arrange the pebbles into two piles so that the following two conditions are both satisfied:

  • The total weights of both piles are the same.
  • Each pile contains two pebbles of each color.

Video solution

https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems]

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