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

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  1. Daniel Sloey on December 18, 2007 at 8:37

    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)

  2. Mitch on January 4, 2008 at 5:00

    hehe i got this one quick­ly :P

  3. Mary A. on January 11, 2008 at 2:34

    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!

  4. kapil on May 30, 2008 at 3:41

    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

  5. Cody on June 23, 2008 at 1:18

    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!!!

  6. Marion on December 6, 2008 at 9:13

    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.


  7. Bill on December 23, 2008 at 8:36

    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.

  8. Martin on December 26, 2008 at 12:14

    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.

  9. Susie on February 28, 2009 at 3:54

    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).

  10. Susie on February 28, 2009 at 3:55

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

  11. dani on March 13, 2009 at 1:14

    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!!!

  12. Eclipse1601 on May 2, 2009 at 8:49

    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

  13. jag61082 on May 11, 2009 at 12:14

    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.

  14. Diana Guillemin on April 3, 2020 at 6:46

    Why not slice the cake hor­i­zon­tal­ly then cut it ver­ti­cal­ly in four pieces

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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.

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