What is the maximum number of pieces you can divide a circular pizza into with 4 cuts? [All cuts must be distinct straight lines from one point on the edge of the pizza to another point on the edge of the pizza, and you may not move the pizza slices.]
Assuming there is no limit on the size of the individual pieces, e.g. NOT x pieces of equal area.
No cut: 1 slice
1 cut: 2 slices
2 cuts: 4 slices (last cut intersects one previous cut, so adds two pieces)
3 cuts: 7 slices (last cut intersects 2 previous cuts, so adds 3 pieces)
4 cuts: (last cut interesects 3 previous cuts, so adds 4 pieces).
... and so on.
To find the maximum number of pieces you can divide a circular pizza into with 4 cuts, you can use the formula:
P = (n^2 + n + 2)/2
where P represents the maximum number of pieces and n is the number of cuts.
In this case, with 4 cuts:
P = (4^2 + 4 + 2)/2
P = (16 + 4 + 2)/2
P = 22/2
P = 11
Therefore, the maximum number of pieces you can divide a circular pizza into with 4 cuts is 11.
To determine the maximum number of pieces that a circular pizza can be divided into using 4 straight cuts, you can use a simple formula.
First, let's consider the first cut. It divides the pizza into two halves.
For the second cut, it can intersect the first cut at a maximum of two points. Each intersection divides the pizza into two halves again. So, after the second cut, we have a total of 4 pieces.
For the third cut, it can intersect both the first and second cuts. There are a maximum of three possible intersections between the three cuts. Each intersection creates a new division in the pizza, resulting in a total of 7 pieces.
Finally, the fourth cut can intersect each of the previous three cuts at a maximum of four points, creating four additional divisions. Hence, the fourth cut gives us 11 pieces.
Therefore, the maximum number of pieces you can divide a circular pizza into using 4 cuts is 11 pieces.