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. eleanor on April 20, 2007 at 1:46

    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, 


  2. Alvaro on April 20, 2007 at 9:53

    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).

  3. George Bell on April 20, 2007 at 2:51

    Hmm, I claim the answer giv­en is invalid as the pieces are not “equal”, they do not con­tain the same amount of frosting!

  4. Caroline on April 20, 2007 at 7:19

    LOL! :-)

  5. Joduba on April 26, 2007 at 11:25

    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 ;-)

  6. Caroline on April 26, 2007 at 11:30

    Sure! That works — espe­cial­ly since it pre­serves the essen­tial frost­ing ratio! Nice job!

  7. john on May 7, 2007 at 3:18

    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.

  8. Caroline on May 7, 2007 at 3:44

    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?

  9. Byron on May 15, 2007 at 12:27

    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…!

  10. Caroline on May 15, 2007 at 12:37

    I love it! I’m com­ing to your house for dinner! :-)

    Maybe I should have used a pic­ture of a pound cake or something!

  11. nameagain on July 24, 2007 at 10:45

    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.

  12. Alvaro on July 24, 2007 at 1:53

    Hel­lo namea­gain, this is sim­ply a lit­tle brain teaser…maybe many peo­ple in the par­ty were on diet?

  13. Jerry P on July 27, 2007 at 5:25

    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.

  14. Caroline on July 27, 2007 at 7:13

    :-) We could all prob­a­bly use a lit­tle less frost­ing anyway!

  15. T Shores on July 29, 2007 at 10:41

    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.

  16. raumi75 on August 23, 2007 at 5:56

    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.

  17. Sunil Kashikar on August 23, 2007 at 9:42

    If we cut the cake this way, 4 peo­ple will end up eat­ing the cake with­out cream, icing and oth­er decoration ;)

  18. Caroline on August 24, 2007 at 8:11

    raumi75 — the cir­cu­lar cuts would be dif­fi­cult, but if done cor­rect­ly, they would work. 

    Sunil — def­i­nite­ly an unfair situation!

  19. aryhel on September 17, 2007 at 9:22

    its so great!!!

  20. Chad W Smith on October 17, 2007 at 8:57

    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!

  21. Jazz on November 6, 2007 at 10:22

    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.

  22. Venkat on November 29, 2007 at 11:11

    Excel­lent web­site with use­ful infor­ma­tion. You got a new reg­u­lar visitor.

  23. Alvaro on November 29, 2007 at 11:36

    Hel­lo Chad and Jazz, that may be more dif­fi­cult to per­form in real life, but it works too…

    Venkat: wel­come!

  24. Silentochestra on November 29, 2007 at 3:21

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

  25. Sycon on December 9, 2007 at 2:35

    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!

English About SharpBrains

SHARPBRAINS is an independent think-tank and consulting firm providing services at the frontier of applied neuroscience, health, leadership and innovation.

English About SharpBrains

SHARPBRAINS es un think-tank y consultoría independiente proporcionando servicios para la neurociencia aplicada, salud, liderazgo e innovación.

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