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This is a trick question. Normally if you wanted to cut a cake into 8 equal pieces you would do so with more than 3 cuts. However, it is possible to do it in 3 cuts if you have a sufficiently long knife. By cutting the cake with two perpendicular cuts you can easily get 4 equal pieces. Then you rearrange these 4 pieces so that they are in a line, with all the pointy ends aligned in the same direction. Then you can cut all four pieces in half with one more cut. But it takes a long knife.

Answer:

Alternately two perpendicular cuts to make 4 equal pieces and a horizontal cut at the middle of the cake to make it into two equal layers each with 4 equal pieces.

But if the cake has frosting on top, then the top pieces can't really be exactly equal to the bottom pieces which won't have frosting on top. Nonetheless, it's a good alternative. And not all cakes are frosted.

Q: How do you cut a cake into 8 equal pieces in 3 cuts?

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In one sense you cannot. The cakes would have a different number of faces which were part of the original faces. To that extent the pieces will not be identical. If such pieces are considered identical, and if the cake pieces can be stacked before cutting, then 9 cuts will suffice. Without stacking, 12 cuts are required. If the cake can be stacked and cut, and a little wastage (less than 2.5%) is pemitted, then 7 cuts will be enough.

-- Adjust the direction of the knife so that it's parallel to the length of the cake,and cut (1) the cake down the middle ... 2 equal pieces.-- Turn the knife 90 degrees so that it's parallel to the width of the cake,and cut (2) the cake down the middle ... 4 equal pieces.-- Stack the 4 equal pieces in an even stack, so that their edges all line up.Cut (3) the stack in two equal pieces, either length-wise, width-wise, oralong either diagonal ... 8 equal pieces.Alternate method for any one of the cuts described above, (1) or (2) or (3):-- Turn the knife so that the blade is parallel to the cake-board and half ofthe height of the cake above the board. Slice through the height of the cake,keeping the knife parallel to the cake's bottom surface, to its top surface andto the cake-board, cutting the whole cake into an upper layer and a lower layerof equal thickness.

If no cut intersects any previous cuts, then you can just slice it into 14 pieces.

Cut a pizza into 2 using one straight cut. Stack the pieces and make a straight cut: you now have 22 = 4 pieces from 2 cuts. Stack these and make a straight cut: you now have 23 = 8 pieces from 3 cuts. Continue. After 7 cuts you can have 27 = 128 pieces. You can reduce the number of pieces to 29 if, after the fourth cut, you stack and cut only 11 pieces and thereafter cut just one each time. There are other options which give the same result.

21 cuts required to cut a cube into 504 identical pieces.

Related questions

use a cutter

Cut a round cake in eight equal sized wedge shaped pieces with four vertical cuts, then make one horizontal cut through the center of the cake to equal sixteen pieces.It's slightly more tricky if you are only allowed to cut the horizontal cross-section of the cake (treat the cake as a circle). In this case, first divide the cake with one cut (2 pieces), then cut it again so that it intersects the first cut (4 pieces), then cut it a third time so that it intersects both cuts previously made, at different points (7 pieces), then let the fourth cut intersect all three cuts so far at different points (11 pieces), and let the fifth and final cut intersect all four cuts at different points (16 pieces total).

You can cut a cake into 16 pieces with 5 cuts by first making a cross-shaped cut dividing the cake into four equal pieces, then cut each of the four pieces in half horizontally and vertically with the last cut.

Cut the cake down the center once. Then cut it down the center again at a perpendicular angle from the first cut. Now you have 4 equal size and shape pieces. Take the pieces and line them all up in a row with each center angle point touching the center of the arc of the next slice of cake. Then cut down the center of each piece in one long continuous cut. There you have it. 8 equal size and shape pieces.

Cut the cake lengthwise and then crosswise. Stack the four pieces and then cut crosswise at one third the length and again at two-thirds the length. Done!

Lets use a square cake to make the instructions easier. Cut one: Make cut parallel to top of cake giving two cake layers Cut two: Diagonally corner to corner Cut three: Diagonally other corner to corner

1) One vertical cut in half.2) A second vertical cut at 90 degrees to the previous one. You should now have 4 equal pieces.3) Make a cut parallel to the table, halfway through the cake. Like you are slicing a bagel in half or a subway sandwich. Should now have 8 equal pieces.4) Eat one piece!

In one sense you cannot. The cakes would have a different number of faces which were part of the original faces. To that extent the pieces will not be identical. If such pieces are considered identical, and if the cake pieces can be stacked before cutting, then 9 cuts will suffice. Without stacking, 12 cuts are required. If the cake can be stacked and cut, and a little wastage (less than 2.5%) is pemitted, then 7 cuts will be enough.

Takes the CakeHere are the steps involved:Cut from 12 o'clock to 6 o'clock (this give you 2 pieces).Cut from 9 o'clock to 3 o'clock (this give you 4 pieces).Cut the cake in half horizontally, slicing through all the pieces. Imagine that you were cutting through the whole cake to put icing in the middle (this give you 8 pieces).

-- Adjust the direction of the knife so that it's parallel to the length of the cake,and cut (1) the cake down the middle ... 2 equal pieces.-- Turn the knife 90 degrees so that it's parallel to the width of the cake,and cut (2) the cake down the middle ... 4 equal pieces.-- Stack the 4 equal pieces in an even stack, so that their edges all line up.Cut (3) the stack in two equal pieces, either length-wise, width-wise, oralong either diagonal ... 8 equal pieces.Alternate method for any one of the cuts described above, (1) or (2) or (3):-- Turn the knife so that the blade is parallel to the cake-board and half ofthe height of the cake above the board. Slice through the height of the cake,keeping the knife parallel to the cake's bottom surface, to its top surface andto the cake-board, cutting the whole cake into an upper layer and a lower layerof equal thickness.

If anything is cut into two equal pieces, it has been bisected.The present tense is bisect.

I can think of 3 ways to do it but none of them seem especially practicable. (1) Cut the whole cake in half laterally through the middle as if you were going to fill it with cream. Then cut it right across through the centre 4 times = 16 pieces. (2) Cut the cake across the middle; make your second cut at right angles to the first through the centre; Bisect those cuts with 2 further cuts each going through the centre. That makes 4 cuts and you now have 8 pieces. Now make a circular cut about 2/3 of the distance between the centre and the perimeter of the cake. To ensure the pieces are equal you'd need to judge carefully the position of this circular cut. (3) Cut the cake in half; stack one half on top of the other; cut this semicircle in half and stack again, you now have a quadrant equal to a quarter of the cake stacked 4 high and you've made 2 cuts. Cut 3 - cut the quadrant in half; Cut 4 bisect the left hand half of the quadrant; Cut 5 bisect the right hand half of the quadrant - voila - 16 pieces - but I wouldn't try it with a gooey cream cake. Is there a particular reason that you can't divide it by making 8 cuts in the usual manner?