6. There are 10 red and 10 yellow apples with a total weight of 1 kg. It is known that the weights of any two apples of the same color differ by no more than 40 g. All apples were sequentially paired "red with yellow," with red apples chosen in non-decreasing order and yellow apples in non-increasing order (i.e., the heaviest red apple was paired with the lightest yellow apple, the second heaviest red apple with the lightest of the remaining yellow apples, and so on). What is the maximum possible weight of a pair?
6. Answer: 136 g. Solution Estimate. Note that the weights of the pairs also cannot differ by more than 40 g. Therefore, if the weight of the heaviest pair is more than 136 g, then the weight of each of the other nine pairs will be more than 96 g, but then the total weight of all apples will be more than 1 kg, which is impossible. Example. Let one red apple weigh 86 g, and the others weigh 46 g each, and each yellow apple weigh 50 g.

Criteria: full solution - 7 points. Only estimate or only example - 3 points. In other cases 0 points.