Brain Out Level 178

Overview

Level 178 asks "At least how many cut to cut a cake into 8 equal pieces?" The board shows a single round chocolate cake on a white plate, with a yellow Enter field and a blue OK button below. Most people answer 4, because four radial cuts through the center of a round cake normally produce 8 slices. But that is only true if you cannot rearrange the pieces. The Brain Out twist is that you are allowed to stack the pieces between cuts, which brings the minimum down to 3: two perpendicular vertical cuts make 4 quarters, and one horizontal cut through the middle splits every quarter in half. The correct answer to enter is 3.

• Difficulty: Regular
• Estimated moves: 2

Step-by-Step Solution

1. Look at the cake and the question. You need 8 equal pieces, and you want the fewest cuts possible.
2. Consider the naive answer 4. Cutting straight down through the center four times at 45-degree angles produces 8 equal wedges, but it uses four cuts. You can do better.
3. Imagine the first cut straight down through the center, splitting the cake into two halves.
4. The second cut is perpendicular to the first, also through the center. You now have four equal quarter pieces.
5. Before the third cut, stack the four quarters on top of one another. A single horizontal cut through the middle of the stack slices all four quarters at once, producing eight equal pieces.
6. Tap the yellow Enter field and type the digit 3. Tap the blue OK button. The level-complete pop-up appears with the line "WOW! That's interesting!" Tap Next to continue.
7. After stacking the three pieces with the first cut, make the second cut horizontally through the stack, then the third cut vertically. All six pieces separate at once.

Continue the action described in the previous steps until the level-complete pop-up appears.
When you stack the cake layers before cutting, make sure all three slices are aligned evenly before you make the first cut. A crooked stack produces uneven pieces, but the game accepts the cut as long as the three pieces are layered on top of one another.

Strategy & Reasoning

The puzzle is a classic combinatorics question disguised as a kitchen problem. With a knife, each cut can at most double the number of pieces if you are allowed to rearrange. Starting from one piece, one cut gives 2, two cuts give 4, and three cuts give 8. The key is that the third cut is horizontal rather than radial. In a real kitchen you cannot easily stack four cake quarters and cut them horizontally, but the puzzle does not forbid rearranging pieces between cuts, and that is the assumption Brain Out wants you to make.

Tips & Common Mistakes

• Answering 4 out of habit. Four radial cuts work, but the minimum is 3 once you allow stacking.
• Trying to enter 8 or 16. Those counts ignore the doubling property of cuts.
• Forgetting that the third cut has to be horizontal. Two vertical cuts alone only make 4 pieces, not 8.