Can you cut a cake fairly to solve this middle school math problem?

[Whateverist]

Now I'm jealous of your ability to illustrate what you have in mind on a computer screen. I think I see what you have in mind but I can't quite see whether it makes a difference. But I think I see a way to investigate it. Let me mess with it a bit and I'll see if I can find a way to show it.

[popeyespappy]

Green, blue and purple gets a whole corner each. Red and yellow have to share one.

[The Valkyrie]

Losty gets to tell the fussy bastards to go fuck themselves and keep the cake for herself (and the kids).

[Whateverist]

[Rev. Rye]

[Jackalope]

As long as Losty used a square pan to bake her square cake and spread the frosting evenly there isn't a problem.

Y'all aren't accusing Losty of sloping the icing on unevenly, are you? I sure hope not because those kinds of accusations have consequences.

I think Chthulthuluuu's point was that if we cut it into five equal rectangular strips lengthwise then besides the issue of the frosting on the end pieces, there would also be less cake on those two end pieces.

Assuming our cutting into five equally thick rectangular strips is based on the external dimensions of the cake as measured on the frosted cake, then the thickness of the frosting itself will be contributing to the thickness of the slice for the end pieces but  not for the three middle pieces.  So, however thick the frosting is applied, that is how much cake the end pieces are not getting.  (Naturally -if I wasn't counting calories- I'd gladly trade that thin slice of cake for extra frosting.)

^^^ This frood knows where his towel is ^^^

[popeyespappy]

Notice that though the yellow and red pieces get only half a corner of frosting, each one gets portion of frosting that extends into the area directly above its neighbor.

OK so I'm making it harder than it needs to be...

I 3d modeled the damn thing and let the computer tell me the volume of all the different parts. A 20x20 cm cake covered with 0.5 cm of icing on the top and sides has a volume of 2425.53 cm. That's 20003 cm of cake and 425.53 cm of icing. If you cut it like we did way back on page 3 everyone gets 4003 cm of cake and 85.13 cm of icing. The thickness of the icing doesn't make a difference as long as it is spread evenly.

Oh, and everyone gets diabetes too from eating that much cake.

[Rev. Rye]

Notice that though the yellow and red pieces get only half a corner of frosting, each one gets portion of frosting that extends into the area directly above its neighbor.

OK so I'm making it harder than it needs to be...

I 3d modeled the damn thing and let the computer tell me the volume of all the different parts. A 20x20 cm cake covered with 0.5 cm of icing on the top and sides has a volume of 2425.53 cm. That's 20003 cm of cake and 425.53 cm of icing. If you cut it like we did way back on page 3 everyone gets 4003 cm of cake and 85.13 cm of icing. The thickness of the icing doesn't make a difference as long as it is spread evenly.

Oh, and everyone gets diabetes too from eating that much cake.

Which is why nobody ever slices their cakes the way the problem suggests. That and it being needlessly counter-intuitive.

[Joods]

While everyone stands around a big white board, drawing schematics and diagrams of how to properly divide the cake Losty made, Nymphadora and her epic stealth skills quickly and cunningly removes said cake from the counter, grabs two forks and two bottles of wine, along with Losty and we sneak out the back door to the deck, where we each grab a seat at the table, facing the house. We each take up a fork and a bottle of wine and laugh heartily at the fools inside who are still bickering about how to cut the cake, and we consume said cake - all without a feeling of guilt because we are women with cake and wine and we are invincible!

And a lot smarter than the men still inside, arguing about the now eaten cake.

[vorlon13]

I still think Losty just needs to make a cake for everyone.

Get cooking, sweetie !!