4. As punishment for bad grades, Vasya's parents sent him to his grandfather in the village. To educate his grandson Vasya, the grandfather first prohibited him from using his smartphone and offered to play the following game. Vasya had a well with water and three buckets with capacities of 3, 5, and 7 liters. Vasya needs to measure out 1 liter of water using these buckets. However, there is a small catch - after every two transfers Vasya makes (filling a bucket counts as a transfer, pouring out any amount of water from a bucket counts as a transfer), the grandfather will definitely pour out the water from one bucket (from any non-empty bucket of his choice, if all buckets are empty, he does nothing). If Vasya can measure out 1 liter of water under these conditions, the grandfather will give him his smartphone. Can Vasya win this game and get his smartphone, despite the grandfather's tricks? (As in all game problems, it is assumed that both sides play correctly).
Answer: Yes, he will be able to.

Solution. Let's denote Vasya's moves with the letter V, and Grandpa's moves with the letter D. See the diagram below.

![](https://cdn.mathpix.com/cropped/2024_05_06_43deb2e742b55dcf0f75g-2.jpg?height=1079&width=707&top_left_y=1390&top_left_x=709)

Criteria. Full solution - 7 points.