7.1. Each of the 37 hexagonal cells has 3, 4, or 6 neighbors. Some of the cells were filled with chips. After that, in each free cell that is adjacent to at least two cells containing chips, the number of these neighboring chips was written. Then the chips were removed, and only the numbers remained on the diagram. How many chips were there?

![](https://cdn.mathpix.com/cropped/2024_05_06_6202285ed0b3c14598f3g-2.jpg?height=711&width=662&top_left_y=887&top_left_x=183)

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# Answer: 8

Solution. Let's look at the picture on the left. Consider the triplet and the central pair. We understand that the chips must be placed at the positions of the yellow crosses. Next, we understand the red minuses - the absence of chips. Then we place the chips at the positions of the green crosses. And the blue minuses - the absence of chips. The purple question mark - can a chip be placed here? We understand that no, because otherwise, at the position of the adjacent blue minus, there should be a 2, but there isn't one. Therefore, we place the chips at the positions of the purple crosses (also considering that no empty cells should be adjacent to two chips, otherwise, there would be numbers in them).

In the end, the chips are placed as shown in the picture on the right.
![](https://cdn.mathpix.com/cropped/2024_05_06_6202285ed0b3c14598f3g-3.jpg?height=986&width=1748&top_left_y=101&top_left_x=198)