Interview Question

Portfolio Management Group-Fixed Income Analyst Interview San Francisco, CA

You have a birthday cake and have exactly 3 slices to cut

  it into 8 equal pieces. How do you do it?
brain teaser

Interview Answer

35 Answers


Cut in half, stack, cut in half, stack, cut in half. All you have to worry about is the 45 degree rotation of one of the 4 pieces after the second cut. Blade can be kept in place, like a paper cutter, as to minimize the margin for error.

z on 20-Dec-2010

Slice it horizontally across the middle creating two equal halves top and bottom.

Then simple two slice cross from above like normal.

Jason on 30-Dec-2010

Cut each slice into 3 slices.
Then eat one of them.

Andrew on 03-Jan-2011

This is really an easy one. First cut into half across the top, then cut the halves in half also across the top (you now have 4 equal pieces) then cut across the middle = 8.

Sharon on 03-Jan-2011

No, Jason and Sharon, you will only wind up with 6 slices. z, too many stacks.
You need to cut in half, then make another cut - to get four pieces. NOW you stack these four pieces and make the last third cut - and you get 8 pieces.

Alina on 11-Jan-2011

A rather easy lateral thinking question. Alina's got it.

Candi on 11-Jan-2011

The stacking seems to be the "right" answer. But this is a stupid question. Who stacks cake? The frosting from the bottom slice would meld with the stacked slice, thus making the cake inseparable.

I wouldn't get the job because I would swear at the interviewer for asking a dumb question. What good is an answer to this question if it wrecks the cake?

J on 11-Jan-2011

Assuming the cake is square:
slice 1: cut horizontally to create 2 equal pieces
slice 2: cut vertically to create 4 equal pieces
slice 3: line up all 4 pieces of cake side by side and cut horizontally to create 8 equal pieces.

don't stack, it will ruin the frosting.

Walter on 11-Jan-2011

With a knife

emw1 on 11-Jan-2011

Alina would be penalized for not being able to count past 6.

But then, she could get a job at another company where they appreciate people who say someone's idea is wrong, then put forth the same idea and take credit for it.

Marty on 11-Jan-2011

A new solution for you: who says slices have to be a straight line and not circular?

I would cut a concentric circle in the middle (would have to calculate the radius compared to the whole), and then slice an X with the remaining 2 cuts. It will look like a target. If done correctly the sizes will be the same, it says nothing about having the same shape!

AZ on 11-Jan-2011

I guess it's much easier if you think of two planes: first cut in half, then to quarters. That's the easy part.

Now look at the cake from the side, and cut it across... Each quarter is cut into two and all pieces are equal.

Etamar Laron on 11-Jan-2011

I would consider the interviewer's emphasis on "equal pieces." While my first thought was to bisect across each of the three dimensions, half of the pieces would end up with less frosting than the other half. Stacking the pieces would result in frosting transfer, which would also screw up some of the pieces. Therefore, I'd go with lining the pieces up and have a large knife on hand for each bisection. Hey, people get crazy about their cake slices.

pt on 11-Jan-2011

I would take a different approach to this. First of all the question asks for the cake to be cut into 8 equal pieces, not 8 identical or 8 of the exact same size. Equal doesn't always have to mean the same, just equivalent to. First I would find out who I am cutting the cake for, if its 4 old ladies and 4 young guys, equal pieces would not mean that they all needed to be the same. If everybody wanted the exact same amount of cake I would figure out a way to give everybody 12.5% of the entire cake volume, but if some wanted larger or smaller pieces I would come up with a way to satisfy each individuals desire.

mike on 11-Jan-2011

If you know how to cut an arbitrary shape in half, you have the solution. After every round, plan the cuts for each individual piece. Then align them so the proposed cuts are in one straight line. Make a cut. This way you can cut any cake into 2^n equal size pieces with n cuts. An interesting question is, if you start with one connected piece, will you always be able to end up with connected pieces. Think of cutting letter S in the middle, like this: $. You end up with two equal figures that are not connected (or, in other words, with 4 pieces). It's also easy to design a cake that can be split into 8 pieces with one straight cut.

Bartosz Milewski on 11-Jan-2011

I LOVE Andrew's answer! Eat one of the freakin' pieces. That's the corporate way in America anyway. Mike is either a socialist, or works in non-profit, or government. I thought "slice them long ways" but then someone misses out on the freaking frosting, which is the best part. UNLESS, it's a layer cake.

Henri on 11-Jan-2011

Cut 'em all in thirds and give the extra to the birthday boy/girl to take home.

Blake on 11-Jan-2011

First I'd yell at whoever cut the cake incorrectly to start with. He's ruining the party. Then I'd squish the 3 pieces of cake together and re-cut the cake into the required 8 pieces. Boom.

Maximus on 11-Jan-2011

This is as easy as pie.
Viewing the cake from the top, make 1 cut vertically down the middle of the cake and another horizontally. Viewing the cake from the side, make your third cut horizontally through the middle; QED three slices and 8 pieces of cake

Bob InNorCal on 11-Jan-2011

with a beamsplitter and prisms it could be done in 1 (with a laser)

let there be light on 11-Jan-2011

That's an oddly presented question that is understood 2 ways:

- 3 cuts allowed to cut one cake in 8 pieces.
 Which yields cut in 4 parts, then split those in 1/2 again with the last cut, either by stacking, realigning the slices or making a round cut.

- 3 pieces of cake must be re-cut to make 8 equal parts.
Which is an impossibility unless one piece is 2/3 smaller than the other 2.
That yields different answers like cutting in 3, and eat one to leave 8 pieces.

Bah on 12-Jan-2011

They key to answering any of the brain teaser questions is to ask a few critical questions before even attempting to answer. I would start with: Is the original cake round or square?

If square, line up all three pieces and recut to be 4 equal widths of cake.

If round, was the original cake cut in 6 or 8 pieces?
If 6 pieces you have 1/4 of a cake = easy to redivide into 8 equal slices.
If 8 pieces, you have 1/3 of a cake and a little math needs to be applied to create 8 equal slices. First slice a strip off each of the 3 slices to create a fourth slice. then divide each in 1/2 to make 8 equal slices.

Anonymous on 12-Jan-2011

Cut each slice into 8 small slices. Then give each person 3 small slices.

Paul Orlov on 12-Jan-2011

There are some posting above who seem to not have a good grasp of numeric's. The answer is not that difficult.
First, presume the pieces are not equal size (nothing states they are).
Second, presume two pieces are of equal size and the third piece is twice that size. Third, cut vertically (the most usual manner in which to cut cake) the 2 equal pieces (we now have 5 pieces -4 the same size and one larger piece).
Fourth, cut the large piece in half, then those two pieces in half again.
Fifth, voila, one now has eight equal pieces of cake.

Cejayem on 12-Jan-2011

Hmmm, I always assumed they meant three knife cuts by the word "slice" Kind of interesting to me that others assumed the cake was given to you in 3 parts as defined by the word "slice"

I'd say that you should cut the cake horizontally using the knife as a measuring device to find the exact center of the circle, then cut vertically using the same method, then take each quarter , using the knife as a straight edge, build an alignment diagram that places each set of two quarter pieces point to point along an axis that defines their center lines, and cut all 4 quarter slices with a single cut of the knife ( defined by the word slice ).

dave on 12-Jan-2011

Put it all in a blender. Pour each of the resultant mixture onto a plate or into a bowl.

Anonymous on 13-Jan-2011

1. assemble 3 sliced cakes into a big cake (original shape)
2. cut it half (don't care about the indentation) , you would get 2 piece of cake
3. cut it half again, you would get 4 pieces of cake
4. cut all of them half again, that's finish.

tumza007lnw on 17-Jan-2011

To those who think it means you start with 3 pieces ("slices") of cake, READ IT AGAIN. It says (emphasis added): “You have a birthday cake and have exactly 3 slices to cut IT into 8 equal pieces." Get it? "... to cut IT [the cake] into 8 equal pieces."... There is NO WAY it means to cut 3 slices of cake, otherwise it would say "...exactly 3 slices to cut into...".

And Mike: "equal doesn't mean same, just equivalent". That's the funniest (and stupidest) thing I've heard all day.

Anyway, since 2^3 = 8, you have to stack. Assuming a round cake:
Cut (or "slice") 1 creates 2 semi-circles.
Stack them.
Cut 2 creates 4 quarter-circles.
Stack then
Cut 3 creates 8 1/8th circles.

SQL Dave on 31-Jan-2011

is the 3 slices equal in size?

X on 10-Feb-2011

Great answer and explanation here:

Steve on 26-May-2011

Make sure the guest of honor has Blown out candles 1st! (was not specified but hey so were many other things) If the birthday boy/girl is under the age of 10, I am not too sure you want to be messing with their cake!!

Cakes come in many different sizes and shapes...ESPECIALLY Birthday Cakes!!!
ACK They even come in characters and shapes you can NEVER get into equal pieces but, back to the solution!
Will use 2 shapes: Round and Square! Cut 1: Parallel to cutting board and horizontal to create 2 layers of equal depth; Cuts 2 and 3: Perpendicular to cutting board once then rotate 90 degrees and repeat!
Now give it to the Kid in the high chair to for quality control/assurance!

seutrvt13 on 04-Mar-2012

Like Andrew, I would eat one piece and then cut the 2 in four equal pieces.

Prosenjit Roy on 09-Aug-2012

Remember 1 whole cake, 3 slices with a knife = 8 equal pieces
Place cake flat on table. Grab a knife big enough to cut the cake horizontally. 1st cut - Cut the cake horizontally leaving the cake flat on table as if the cake still in one single piece. Now you have 2 cakes instead of one.
2nd and 3rd cut - cut through the cake vertically in the form of a cross. Now you have 8 equal pieces of cake. As if you had cut 2 cakes in 4 pieces each.

Ariel on 03-Oct-2012

I would state that I only eat cakes in the shape of circle. then 3 equal cuts across the middle. think of it like a pizza... or a pie.... or a pizza pie.

Remember these questions are made to have you think outside the box. Not all cakes are square.

Anonymous on 25-Apr-2014

cut the diagonal portion then centre line of cake

palak on 27-Sep-2014

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