[mjd]

That's an interesting theory but I don't think I find it plausible. Say we're cutting bars like you said. With the obvious strategy I have to cut the three bars into a total of 9 pieces of sizes no less than 1/3 bar each: I cut two of the bars into pieces of 3+3+1 and one bar into pieces of 3+2+2. Then I give five of the people the size-3 bars, and the other two people each get 2+1.

The two people getting the 1/7 + 2/7 pairs can easily verify they are not getting shortchanged, simply by putting their next to one of the 3/7 bars to make sure they add up to the right length.

(Someone dividing 7 sacks of grain among 3 people can do something similar. Maybe they compare two shares of grain on a balance.)

But if you're trying to give everyone a 1/4 bar, a 1/7 bar and a 1/28 bar, sure, it's “trivially obvious to be fair” if you believe you can divide a 1/4 bar into seven exactly equal pieces. But you can't, some will be a little bigger and some will be a little smaller. Seriously, have you ever tried to cut something us unmanageable as a metal bar into seven equal pieces?

[EdwardCoffin]

On the other hand, the bars have to be cut no matter which strategy one uses, so this criticism of not being able to cut the bars into exactly equal pieces applies equally to the other strategies.

This Egyptian strategy definitely does have a property of being easier to reason about, and one doesn't have to contend with complaints of say losing out on small amounts of metal around the cuts when one is given three smaller bars that put end-to-end are as long as another, but whose internal mating surfaces don't match up exactly.