Difference between revisions of "2020 IMO Problems/Problem 3"
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− | Problem | + | == Problem == |
− | + | 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: | + | * The total weights of both piles are the same. |
− | + | * Each pile contains two pebbles of each color. | |
− | |||
== Video solution == | == Video solution == | ||
https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems] | https://youtu.be/bDHtM1wijbY [Video covers all day 1 problems] | ||
+ | |||
+ | ==See Also== | ||
+ | |||
+ | {{IMO box|year=2020|num-b=2|num-a=4}} | ||
+ | |||
+ | [[Category:Olympiad Combinatorics Problems]] |
Latest revision as of 11:31, 14 May 2021
Problem
There are pebbles of weights . Each pebble is colored in one of 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]
See Also
2020 IMO (Problems) • Resources | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 4 |
All IMO Problems and Solutions |