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Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2010 All-Russian Olympiad Regional Round
11.2
11.2
Part of
2010 All-Russian Olympiad Regional Round
Problems
(1)
2009 integer weights <=1 kg
Source: Russian Regional Olympiad 2010 11.2
8/24/2024
In a row of
2009
2009
2009
weights, the weight of each weight is an integer grams and does not exceed
1
1
1
kg. The weights of any two adjacent weights differ by exactly
1
1
1
g, and the total weight of all weights in grams is an even number. Prove that weights can be separated into two piles, the sums of the weights in which are equal.
combinatorics