Marc Ordower
Region: US
Friday 23 May 2025 21:50:31 GMT
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Corey :
It is mathematically possible. They won’t be uniform cuts but yes
2025-05-23 21:58:12
98
Emzy :
Cut it into 4, remove one piece and done
2025-05-24 00:21:14
109
Dikran Torian :
Yes, same amount of cake. No, on the same amount of frosting. But if you put frosting on the bottom as well, then yes.
2025-05-25 10:07:47
2
f.......f......f :
if you look from the 1,1,1 position of the cake towards 0,0,0 it looks like a hexagon, so chop it into 120 degree sectors, it's gotta be the same thing for each
2025-05-24 18:52:54
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mmkayultra :
Making a v cut on the top, you could make the center piece have either more or less cake and frosting than the outside pieces, so there must be an angle which is equal
2025-05-23 21:59:43
8
ashtonkelley14 :
no because thirds don't exist
2025-05-23 23:43:04
2
Michael :
Is the cake frosted on the bottom side too?
2025-05-23 22:28:52
17
knockonwoodrow :
I'm pretty sure you can do it with two cuts, same frosting and volume, but not the same shape: 1) Rotate the cube so you're looking at one flat side (a square). You *could* make two vertical cuts and easily divide the cake into three pieces, but that wouldn't have equal frosting. 2) Instead, line up a single cut from the top-left corner to a point on the bottom ⅔ of the way from left to right. This diagonal is still a third of the total volume, but it's now also a third of the frosting. 3) Remove the piece, and rotate the remaining cake 90°, then cut it in half at the midpoint. All three pieces will have 5/3 side's worth of frosting, and ⅓ of the total volume
2025-05-27 12:40:28
1
Mav D :
do we have to stay in the Euclidean plane?
2025-05-23 21:57:54
5
Laurence Jay :
Just put it up on one of its angles. Look from upside and you will see three edges. Just cut vertically following those edges. You can see those three edges and the top angle pointing at you in the post’s picture
2025-05-24 16:11:58
1
Invinsul :
the frosting is the part that threw me off. is the solution to do with using a line scored to find the centre point maybe. im usually pretty good at your puzzles but i will admit im struggling with this one
2025-05-24 12:49:54
1
BobbyD :
Each piece needs 2 sides worth of frosting, so starting from a corner, cut toward the center of the cube and follow that edge with the knife edge remaining in the very center. Follow the edge for 2 adjacent sides and all 3 pieces will be an L
2025-05-24 19:31:04
1
michelsauve :
Yes: think of each square face as composed of 3 congruent rectangles. Let top be ABCD. Let EF be directly below C and D one third of the way down on those edges. Make a straight slice exposing rectangle ABEF. That wedge has five « rectangles » of icing.(3 on top, 1 vertical, and 2 vertical triangles). The remaining cake has ten rectangles of icing and is symmetrical. Just do a vertical slice through mid points of AB and EF.
2025-05-24 15:56:08
0
Valdr :
Ham Sandwich Theorem so yea I guess
2025-05-25 02:19:20
0
Joc :
Imagine it cut into 6 pyramids by using a triangular knife at a 45degree angle at each edge, so that each side of the cake is the base of a pyramid, the bases all have the same frosted base and a pyramid of cake, then just don't cut the adjacent edge of any three adjacent pyramids. Each slice of the three slices would be effectively two identical pyramids stuck together
2025-05-25 00:16:28
0
Hans Melby :
You could cut off a pyramidal corner and then split the remaining cake.
2025-05-23 23:54:43
1
Teaknee :
take all the icing off, cut into 3 equal slabs, then weigh the icing make 3 equal portions and then put cake on top
2025-07-05 21:48:28
0
Avocategory :
Yes. Lemma: it suffices to divide a square into 3 pieces with equal area, and which have equal portions of the original perimeter, because original perimeter measure side frosting, and area measures cake and top frosting.
2025-05-23 22:00:52
1
DatDragonOne :
if all the cuts are vertical this is the same problem as dealing with a square cake and you want all 3 people to have same amount of cake and the same amount of edge peice mark 3 points on the perimeter of the top of the cake such that they partition the perimeter into 3 equal lengths draw a line from the centre of the square to each of those marks and cut down on each line this gives 3 peices with equal frosting and volume the frosting on the sides is equal because of the dividing perimeter thing the shapes made by the lines on the top can be cut into triangles with all the same height and the sum of the bases of each triangle from each shape is the same so they have the same area so the volume and top frosting is the same
2025-05-23 22:01:21
2
surfing_guy_LE :
I would rather take the biggest piece of cake with the lowest amount of frosting ♥️
2025-05-24 05:55:48
0
Stephen Wood :
I tried to find a solution using just 2 vertical cuts. But, it seems there is no such solution. The idea is to cut off a triangle or trapesium of the top square that includes ⅓ of the perimeter and ⅓ of the top area. Then you can cut the larger piece in half with ⅓ perimeter & area in each part. For the first cut (assume a unit square): - If a triangle, pick two points on adjacent sides distance (1-d) & (⅓+d) from the mutual corner, where 0<=d<=⅓. This always covers 4/3 units perimeter, which is perfect, but the area varies between min of ⅙ and max of 2/9. We need ⅓, so not possible. If a trapesium, then picking points s.t. 4/3 apart around the perimeter gives a fixed area of ⅙ unit². So, again not possible. If there is a solution it involves non-vertical cuts.
2025-05-24 15:44:46
0
e :
You can have 3 pieces with the same amount of cake OR the same amount of frosting... it's impossible to have both
2025-06-08 17:37:38
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anonimolice :
from the top view, if you cut from bottom corner into the middle of the top side, you can ensure that each cake has 1 full size, now you just need to cut so that each cut has 66% total from two sides
2025-05-24 18:12:58
0
James McDowell :
yes, at least I'm pretty sure my working out is right, I'd love to see that actual answer to compare 😁
2025-06-14 22:38:48
0
Joe JJ :
yes. the three planes intersect on the diagonal corner to corner.
2025-05-24 13:20:05
0
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