Question 91
2009 Weights Are Placed in A Row. Each Weight Is of Integer Number Of Grams, and No Weight Is Heavier Than 1 kg. It turned out that each neighboring weights differently 1 g, while the total weight of all weights (in grams) is an even number. Prove that it is possible to partition all the weights into two sets with equal total weights. In the series of 2009, the weight of each weight is an integer number of grams and does not exceed 1 kg. The weights of any two neighboring weights differ exactly by 1 g, and the total weight of all weights in grams is an even number. Prove that weights can be divided into two piles, the sum of the weights in which are equal.