25. A chocolate bar consists of $5 \times 8$ square pieces. The bar is broken along straight lines, separating the pieces, until 40 individual pieces are obtained. How many times will the bar need to be broken? (Find all solutions.)
25. Each time we break one piece, we get two smaller pieces, i.e., the total number of pieces increases by one. Initially, there was one piece. Therefore, we will have to break the chocolate bar 39 times.

![](https://cdn.mathpix.com/cropped/2024_05_21_7d0959e1f193b6338b84g-41.jpg?height=834&width=1010&top_left_y=271&top_left_x=340)

Fig. 25.

![](https://cdn.mathpix.com/cropped/2024_05_21_7d0959e1f193b6338b84g-41.jpg?height=796&width=778&top_left_y=275&top_left_x=1600)

Fig. 26.

![](https://cdn.mathpix.com/cropped/2024_05_21_7d0959e1f193b6338b84g-41.jpg?height=643&width=1357&top_left_y=1309&top_left_x=735)

Fig. 27.

![](https://cdn.mathpix.com/cropped/2024_05_21_7d0959e1f193b6338b84g-41.jpg?height=695&width=1100&top_left_y=2143&top_left_x=856)

Fig. 28.