1.4. In Zhenya's black box, there are 8 bananas and 10 mangoes, and in the white box - 12 mangoes. In one move, Zhenya, without looking, can take a fruit from any box and either eat it or move it to the other box. Zhenya wants the contents of the boxes to be the same. What is the minimum number of moves Zhenya can guarantee to achieve this? The boxes are closed, and the fruits cannot be identified by touch.
# Answer: 24

Solution. Suppose that in the end, both boxes still contain both bananas and mangoes. Then the last action was Zhenya taking some fruit from a box, and both types of fruit remained. Because of this, she could not guarantee picking the right fruit, as she might have picked the wrong one.

If removing mangoes, it would require a minimum of 22 actions, and if removing bananas - a minimum of 18 actions, since bananas might be at the bottom of the box. In this case, there would be between 12 and 22 mangoes left in the white box, and it would take at least 6 more actions to sort them. Example: remove everything from the black box, and then transfer 6 mangoes from the white box to the black box.