Question 73
Some family pairs are friends with each other. Every St. Valentine's Day each husband of these pairs presents some roses to each wife of these pairs (including his own wife). Any wife will be offended by her husband if the number of roses that she obtains from her husband is less than or equal to the number of roses that he presents to all other wives together. This year, it turned out, that for any wife there is a partition of all husbands into two groups such that the total numbers of roses that are presented to this wife by the men from each group are equal (the groups may be different for different women).
Prove that at least one wife will be offended.
Prove that at least one wife will be offended.