Apr 20, 2007
Mental Imagery and Spatial Rotation Brain Teaser
By: Caroline Latham
Here’s a fun puzzle that a friend gave me over dinner a few days ago …
How do you cut a cake into eight equal pieces with only three cuts?
the cake in the puzzle is not necessarily the one pictured below
You have to use your mental rotation and mental imagery skills to visualize the answer for this puzzle. In doing so, you are using your visual cortex in the occipital lobes, your somatosensory cortex in your parietal lobes, and your executive functions in your frontal lobes to help create and evaluate your hypotheses.
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Answer: Use two cuts to cut the cake into four equal pieces. Use your third cut to cut the four pieces in half horizontally (perpendicular to the first two cuts).
That is a clever one!
What is your stance on ‘smart drugs’? They are in the media a lot over here at the moment and I thought of SharpBrains and wondered what your take on it was.
All the best,
Eleanor
Hi Eleanor:
Our stance it that it is way to early to say. In general we prefer natural, non-drug, methods to exercise and improve our minds, because we know how they work and don’t have side effects.
We are skeptic about “miracle pills” for healthy individuals, but are open minded and willing to see results from longitudinal studies that may show the efficacy and lack of side-effects of “smart drugs”.
Nothing beats some good exercise (physical and mental).
Hmm, I claim the answer given is invalid as the pieces are not “equal”, they do not contain the same amount of frosting!
LOL!
Can I move the slices ?
If so, I can do it, by aligning 2 slices with the other 2 and having 4 slices aligned…
With that method, I have the same frosting in all cuts
Sure! That works — especially since it preserves the essential frosting ratio! Nice job!
Maybe I’m retarded, but I don’t get how you get 4 pieces of cake w/2 slices, unless you cut once vertically & once horizontally. If you do that how can you make a perpendicular cut to both? Thanks for helping.
Good question John. The first two cuts are perpendicular to each other in the same plane (X and Y axis, if you will). The third cut is in the Z axis, in a perpendicular plane. If you had a layer cake, essentially you would be splitting the layers. Does that make sense?
I suppose I’m part of the crowd who didn’t solve the puzzle because we wouldn’t dare serve the four bottom slices in fear of getting dirty looks from the four recipients.
Multi-tier cakes on the other hand…!
I love it! I’m coming to your house for dinner!
Maybe I should have used a picture of a pound cake or something!
maybe i am retarded but it is such a waste of life to get only 8 pieces out of a birthday pie which shows that the person of the party is old enough to have an army of friends and young enough to have most of his family members alive.
Hello nameagain, this is simply a little brain teaser…maybe many people in the party were on diet?
I got up in the middle of the night, took another look at the cake, and finally realized how to do it.
People would be better off not worrying about the frosting and just do the exercise.
intersting–and not an option most would think of, as the lower “slices” are not really slices per se. it should say. but i guess the whole idea is to think outside the box, or cake in this example.
Given it is a circular cake, you could make one round cut in the middle (shape of an O) and then make two cross cuts (shape of an X). That would leave every piece with an equal amount of frosting if you choose the inner diameter correctly.
If we cut the cake this way, 4 people will end up eating the cake without cream, icing and other decoration
raumi75 — the circular cuts would be difficult, but if done correctly, they would work.
Sunil — definitely an unfair situation!
its so great!!!
Couldn’t you just stack the pieces after each cut?
cut 1 = 2 equal pieces
Stack them
cut 2 (just like a normal cake) in half again = 4
Stack the 4 pieces
cut 3 = 8 equal pieces. (with the same amount of smeared frosting!
[…] Comment on Mental Imagery and Spatial Rotation Brain Teaser by …Couldn’t you just stack the pieces after each cut? cut 1 = 2 equal pieces. Stack them cut 2 (just like a normal cake) in half again = 4. Stack the 4 pieces cut 3 = 8 equal pieces. (with the same amount of smeared frosting! […]
[…] 23. Mental Imagery and Spatial Rotation challenge. […]
I don’t understand the final cutting part in the answer but i thought of the same thing as Chad W Smith.
Cut the entire cake across twice first like an “x”, then stack them like a tower and cut all the way down.
Excellent website with useful information. You got a new regular visitor.
Hello Chad and Jazz, that may be more difficult to perform in real life, but it works too…
Venkat: welcome!
This is an awesome site. I didnt get this one until i read the comments, lol. Luckily its not just me
Well, first off this is an awesome site. Second, my original solution involved making a circular cut after dividing the cake into 4 pieces. Of course this requires a circular cake (a different cut would be needed for a square/rectangle cake) and you would have to figure out the halfway point volume area-wise.
So far I think the best solution is to cut the pieces, line them up and cut them in half, need lots of frosting!
This is a clever one.
Cut 1: cut cake in half.
cut 2: cut cake to make 4 equil pieces
cut 3: cut the cake in half (top and Bottom)
hehe i got this one quickly
Unless it’s homemade frosting, it’s probably loaded with high fructose corn syrup and maybe even trans fats…all terrible for our brain health. Better to have the even slices using the “two layer” method and take one from the bottom half!
first cut it from top in to 4 parts equally then youwill get 4 parts and now cut at side in to halfs no you will get 8 parts
First you cut the cake down then,wiyhout bringing your knife up make a K and cut a line from the middle of the K.
Then you do the same thing with the other side but this time bring the knife up after you have your backwards K and make a cut in the middle of the K.You’ve made 3 cuts and have 8 slices!!!
I gave this problem to a student of mine many, many years ago. He came up with an answer that I believe is more correct than the standard answer. If equal means “like in quality, nature, or status” and also being the same in every way then his answer would be better. His answer was the same as yours for the first cut and the second cut. His answer differed re: the third cut. He said you would have to take out each of the four pieces and put them on top of each other (assuming you have made something that would hold all the pieces steady). Then you would make the third slice down from the top of the pile through to the bottom. You would then have four
“equal” pieces because they would all have icing on their top.
Cutting through the middle as the third cut would not allow the last four pieces to have icing on them, thereby not being “equal” to the others.
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I had a better solution (in my opinion anyway).
1) Cut the cake equally into four pieces (2 cuts)
2) Place the four equal pieces on top of each other.
3) Cut through the middle of the four layers of the cake quaters (Third cut) making eight equal pieces.
Cut the cake in half (so it creates two stacked cakes). Then simply make an “x” on the top of the cake. You will end up with 4 pieces stacked on top of 4 pieces.
I hope I am not reiterating anyone’s idea. My thought is to first cut horizontally through the entire cake at the vertical midpoint. Take the bottom layer that was just made and put it on top. Press the new “top” layer so that the icing is in between the two tiers. Then make two vertical cuts perpendicular to one another. If the top tier was pressed so that the icing was spread out evenly each of the 8 pieces should have the same amount, including any little swirly icing rings that were around the circumference of the bottom of the original cake (assuming it was a circular cake).
P.S. I didn’t say it would be a pretty cake.
umm…you can’t cut a cake 3 times and make 8 slices,sorry,it can’t be done! you have to cut it 4 times in order to get 8 slices!!!
if you cut the cake horizontally (transverse) across the middle…that’s one slice.
The other two slices can be cut perpendicular to each other.
This will give you 8 pieces
The correct answer is to stack the 4 equal pieces and to cut them straight down.
My 9 year old daughter was so angry that she couldn’t figure this one out. LOL. She actually took out graph paper and a pair of scissors to try to work it out. She is making her mama proud!
This website is great for adult and children’s brains alike. I had to think about this one for a while.