Prime partitions

I bake a lot of bread, 2-8 loaves a week, and I'm cutting bread a lot. I usually freeze freshly baked bread to keep it from going immediately stale, and I cut the bread before I freeze it because it's impossible to cut frozen bread.

One of the loaves I like to make is my cranberry pumpkin seed bread. I eat a bit of this bread every day for lunch, and I've been doing this for a decade. In an effort to cut down on (or at least measure) the amount of carbs I'm consuming I've started cutting smaller slices from my baguettes.

The recipe uses 1200g of flour and produces 4 loaves. I cut each of these loaves into 10 pieces which gives me a small (30g of flour) hunk of bread for my lunch each day.

I've noticed when cutting bread that it's more difficult to cut into larger prime partitions:

• Cutting a piece in 2 is easy, just cut down the center.
• Cutting a piece into 3 can be measured by eye
• Cutting a piece into 4 is easy, cut it in half and cut each piece in half again. This is essentially factoring the bread. (2 * 2)
• Cutting into 5 is getting hard.
• Cutting into 6 is relatively easy - cut in half and then each piece into thirds. (2 * 3)
• Cutting into 7 is pretty difficult.
• Cutting into 8 is easy (2* 2 * 2).
• Cutting into 9 is relatively easy (3 * 3).
• Cutting into 10 is as difficult as cutting it into 5 pieces (2 * 5).
• Cutting into 11 is impossible.
• Cutting into 12 is easy (2 * 2 * 3)
• Cutting into 13 is impossible.

Incidentally the multiplicative property of this bread factorization is commutative (2 * 5) = (5 * 2). To cut my loaf into 10 pieces I cut it in half first and then cut each piece into 5, generally cutting out a slice in the center and then cutting the two remaining ends in half. I could cut the large loaf into 5 pieces and then cut each of these into half but for some reason it seems more difficult to do it this way.

I accidentally left my bread proofing overnight and the baguettes were like deflated tires in their couches when I checked on it in the morning, but I baked them anyway, and they turned out alright. While the freshly baked loaves were still cooling on the counter, Amanda asked if she could have a slice and I had to run in to slice it for her because she hadn't read this post, and it was too hard to explain all this from the other room.

posted by na on April 23, 2024 07:21