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Mental Imagery and Spatial Rotation Brain Teaser

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

mental rotation task

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.

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).

PS: Enjoy these 50 brain teasers to test your cog­ni­tive abil­ity. Free, and fun for adults of any age!

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40 Responses

  1. Silentochestra says:

    This is an awe­some site. I didnt get this one until i read the com­ments, lol. Luck­ily its not just me 😀

  2. Sycon says:

    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!

  3. Daniel Sloey says:

    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)

  4. Mitch says:

    hehe i got this one quickly 😛

  5. Mary A. says:

    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!

  6. kapil says:

    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

  7. Cody says:

    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!!!

  8. Marion says:

    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.


  9. Bill says:

    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.

  10. Martin says:

    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.

  11. Susie says:

    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).

  12. Susie says:

    P.S. I didn’t say it would be a pretty cake.

  13. dani says:

    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!!!

  14. Eclipse1601 says:

    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

  15. jag61082 says:

    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.

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