1. Three bees collect nectar from 88 garden flowers. Each flower was visited by at least one bee. Each bee visited exactly 54 flowers. We will call a flower sweet if it was visited by all three bees, and bitter if it was visited by exactly one. Which of these 88 flowers are more: sweet or bitter, and by how many?
Solution. Let among the 88 garden flowers, $s$ be sweet and $g$ be bitter. Then the number of flowers visited by two bees is exactly $88-s-g$. On one hand, the total number of bee landings on the flowers is $3 \cdot 54=162$ (each bee visited 54 flowers), and on the other hand, it is $3s + 2(88-s-g) + g = s - g + 176$. We have the equation $162 = s - g + 176$, from which $s - g = -14$. This means that there are 14 more bitter flowers. Answer: there are 14 more bitter flowers.