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. Stack the four pieces vertically, and use your third cut to cut the four pieces in half horizontally.

**Next brain teaser:**

- #18. How many…

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.