You are given a piece of paper, and your task is to cut it into 8 equal pieces. The challenge is to determine the minimum number of straight cuts required to achieve this. The cuts can be made in any direction, but the pieces must remain stacked together throughout the process.

Objective:
Find the minimum number of straight cuts needed to cut the paper into exactly 8 equal pieces.

Solution

To solve this puzzle, we need to understand how each cut can maximize the number of pieces created while minimizing the total number of cuts. The key lies in using the previous cuts effectively by stacking the pieces and cutting them simultaneously.

Step-by-Step Solution for Minimum Cut Puzzle:

Step 1: First Cut

Start with a single sheet of paper. The first straight cut will divide the paper into 2 equal pieces. This is straightforward, as any single cut through the paper will always result in two pieces.

• Number of pieces after 1st cut: 2

Step 2: Second Cut

Stack the two pieces on top of each other. The second straight cut, when applied to the stacked pieces, will now divide each piece into 2 more pieces. Since the two pieces are stacked, this cut will result in a total of 4 pieces.

• Number of pieces after 2nd cut: 4

Step 3: Third Cut

Next, stack all four pieces together. The third straight cut, when applied to this stack, will again divide each piece into 2 more pieces. Since you are cutting through all four pieces simultaneously, this cut will result in a total of 8 pieces.

• Number of pieces after 3rd cut: 8

Step 4: Final Answer

After making three straight cuts while stacking the pieces each time, you will end up with 8 equal pieces of paper.

• Total number of cuts required: 3

This is the minimum number of cuts needed to divide the paper into 8 equal pieces.