Most pieces of pancake from six straight cuts

Question

You have a round pancake and a knife. Each cut is a single straight line all the way across, and you are not allowed to move or stack the pieces between cuts, every cut is one straight slice through the whole arrangement.

What is the greatest number of pieces you can end up with after 6 straight cuts?

Accepted Answer

The maximum is 22 pieces. Add cuts one at a time and count the gain. Start with 1 whole pancake (0 cuts). Each new cut adds the most pieces when it crosses every previous cut at a distinct point inside the pancake, because a line that crosses k existing cuts is itself divided into k+1 segments, and each segment slices one existing region into two, adding k+1 pieces. - Cut 1 crosses 0 previous cuts → adds 0+1 = 1 piece → total 2. - Cut 2 crosses 1 → adds 2 → total 4. - Cut 3 crosses 2 → adds 3 → total 7. - Cut 4 crosses 3 → adds 4 → total 11. - Cut 5 crosses 4 → adds 5 → total 16. - Cut 6 cros…

Most pieces of pancake from six straight cuts

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