Submitted by the reader:
You have a sheet cake. There is a rectangular piece missing from the inside of the sheet cake. The location of the missing piece is arbitrary. I was told I could assume I had the means to make the cuts. How do you divide the sheet cake into 2 even proportions with 2 cuts?
17 Comments on Cake puzzle
Take a rectangular sheet and assume we make a square cut at the center of it. then we make 2 cuts on the rectangle from the center of the rectangle going thru the middle of the sqare. rectangle will be divided into two equal halves with 2 cuts as per the requirement.
that last comment did not make sense. if you have a sheet cake with a rectangular piece missing from the center, you make two cuts (as you are allowed) from a corner of the outer edge of the sheet cake to the corresponding corner of the rectangular missing section. Repeat on the diagonal corner. This way, it doesn’t matter what size or shape the rectangle is…
Read directions before you post comments!!!
“The location of the missing RECTANGULAR (not square) piece is ARBITRARY (not necessarily in the center).
Now that’s something to think about…
I don’t know about 2 cuts, but I could do it in one cut. That would be the best I could come up with…look at the cake sideways, at eye level while it’s sitting on the table, and cut it in half (left to right or right to left), horizontally on a plane. Interested to see what the real answer to this one is.
I can’t proove I’m correct… but here goes:
Imagine the rectangle-hole in the centre of the rectangle-cake and with the sides of both rectangles parallel (it *will* work for arbitary positions, bear with me). Cut from the top-right corner of the cake inwards to the top-right corner of the hole. Then make your 2nd cut from the bottom-left cake corner to bottom-left hole corner.
Obviously this halves the cake.
It also works if the hole if rotated and/or off-centre! However you must cut first between the two nearest corners (the shortest cut), and then the corners opposite this - which I think is the longest cut, this halves the cake too.
To prove KT wrong…
Imaging a very narrow (compared to the width of the cake) rectangular piece cut out right next to one of the sides. Make the length 3/4 of the length of the cake. Your solution doesn’t work in this and many other instances.
I agree with G. Dawson (#4) on the solution. This is also what my friend came up with. If you are asked a question like this, it’s most likely to be tricky, and not a simple geometry problem. They want to see your ability to think outside the box and come up with alternative solutions with less resources (1 cut vs. 2).
From what I heard, this sounds like something Google recruiters might ask…
Yes, Vitali is correct!
My answer is completely wrong.
Here’s two correct answers :)
(1) Measure both the rectangles, subtract the hole’s area, then make two cuts such that the remaining area is halved. Your cuts must pass though the hole, otherwise you can only make one cut.
(2) Balance the sheet/cake over a long fulcrum until it falls to neither side, but such that the path of the middle falls through the hole (so you can make two cuts). Slice the cake along the line of the fulcrum. Your fulcrum could be the edge of a table for instance. It might be pointed out that the cake has a non-uniform density so this doesn’t work - but this brings the question back to the notion of ‘half’ - by area or by weight.
-kt
Cut Horizontally, one cut. Done.
Find center of the cacke (rectangle). Find the center of missed rectangle.
And cut on the straight line which should go through both points.
That cut will give exactly two equal halves.
How: Any straight line going through center of rectangle cuts the rectangle in two equal halves.
Two Steps
1. FIRST CUT: Cut another rectangle out (same size as the original cut) diagonally opposite to the other one so that the cake is balanced.
2. SECOND CUT: Cut any way across the cake (diagonally, horizontally or vertically)
You should have two equal pieces.
Ravi,
That leaves you with three pieces as the rectangle you cut out is a piece. If you able to discard pieces of cake then there are loads of solutions.
cut along the line joining the center of the piece and the original cake.
this is the solution..
rocky
Draw a line which pass from the center of the cake and splits the rectangel in 2 exact part.
100 word(19 to be exact) = 1 picture
http://flickr.com/photos/tina_maulin/276979708/
Hi, It’s more simple
Step 1.- Cut the cake passing by the 2 oposite corners of the rectangle.
Step 2.- Cut the cut before by the perpendicular angle in the midle of the cut.
Finally you have 4 pieces of cake; 2 without the rectangle piece and 2 with the reactangle piece. Take one with the rectangle and other without the rectangle. And you will finish!
Koti’s answer is correct. Other may have either some assumption or the variation of the following answer.
Find center of the cake (rectangle). Find the center of missed rectangle.
And cut on the straight line which should go through both points.
That cut will give exactly two equal halves.
How: Any straight line going through center of rectangle cuts the rectangle in two equal halves.
-Navin
We can do it with a single cut. A horizontal cut. which pass through the centre of the cake flat an parallel to the top and bottom sided of the cake. If you want to make it by two cuts. Divide the one cut in to two :-)
I agree with one solution. And I have confirmed it’s accuracy in “How to move mt. fuji” book which presents this problem and it’s solution.
The CORRECT solution is ONE CUT. Through the centers of both the outer and inner rectangles.
If you cut horizontally, then who gets the ICING and who eats the not-so-yummy base ;)