How to Divide a Cake Without a Fight?

Split Equally Without Complaints!

Siblings are always fighting. Especially when it comes to dividing a cake between two. "Mine's smaller!" "Yours is bigger!" To split a cake between two without complaints, you can use the "I cut, you choose" method. After dividing, if one complains, you can say, "Well, you did the cutting" or "You made the choice." If you have siblings, why not give this method a try?

What About Three or More People?

Dividing among three gets a bit trickier.

Step 1:

Tom divides the cake into two parts, X and Y. By Tom's judgment, X is worth 1/3 of the cake, and Y is worth 2/3.

Step 2:

Dick observes X. If he thinks its value exceeds 1/3, he trims it to exactly 1/3. If it's worth less, he does nothing. The modified or unmodified piece is denoted as X*.

Step 3:

Harry checks X*. If he feels its value is at least 1/3, he takes it. If not, he leaves it.

Step 4:

• (a) If Harry takes X*, Tom and Dick see the remaining cake as one piece (including any trimmings from X) and follow the "I cut, you choose" method.
• (b) If Harry doesn't take X* and Dick had trimmed X, then Dick takes X*. Tom and Harry apply the "I cut, you choose" method to the remaining cake.
• (c) If Harry doesn't take X* and Dick didn't trim X, Tom takes X. Dick and Harry then apply the "I cut, you choose" method to the remaining cake.

From "Divide, Stuff, Color - Read and Learn Mathematical Thinking" p.19.

The "trimming" method makes sense. There are other methods for three or more people. And these methods can also be extended for four or more.

For a detailed explanation, see "Divide, Stuff, Color - Read and Learn Mathematical Thinking."

It's Not Just About Cake

These methods aren't limited to just cake but can be applied to inheritance division or territorial disputes.

Real-life scenarios can be more complicated, and this method might not solve everything.

References

• How to Cut a Cake: And Other Mathematical by Ian Stewart