Mental Imagery and Spatial Rotation Brain Teaser
April 20, 2007//
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. Stack the four pieces vertically, and use your third cut to cut the four pieces in half horizontally.
Next brain teaser:
- #18. How many…
Posted in Brain Teasers
39 Comments
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SHARPBRAINS is an independent think-tank and consulting firm providing services at the frontier of applied neuroscience, health, leadership and innovation.
SHARPBRAINS es un think-tank y consultoría independiente proporcionando servicios para la neurociencia aplicada, salud, liderazgo e innovación.
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.
:-) We could all probably use a little less frosting anyway!
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!
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 :D
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!