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#20. Pattern Recognition Brain Teaser — The Empty Triangle

Please enjoy this brain teas­er com­pli­ments of puz­zle mas­ter Wes Car­roll.

The Emp­ty Tri­an­gle

Pattern Recognition Test - Empty Triangle

Which fig­ure should be placed in the emp­ty tri­an­gle?

This puz­zle works your exec­u­tive func­tions in your frontal lobes by using your pat­tern recog­ni­tion, hypoth­e­sis test­ing, and log­ic. Let us know how you do!




The top num­ber minus the bot­tom left-hand num­ber is mul­ti­plied by the bot­tom right-hand num­ber to give the num­ber inside the tri­an­gle.

Next brain teas­er in Sharp­Brains’ top 25 series:

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54 Responses

  1. rob says:

    i came up with the same answer as kevin the sums added across all equal 26 if 6 is placed in the tri­an­gle.

  2. Toffee says:

    Anoth­er option if you look at it as a set…
    (6–2)+ (6–2) = 8
    (7–5) +(7–3) = 6

    For the third one and fourth as a set fol­low the same rule

    (7+4)- (7–2)= 6
    (6+5) — (6–3) = 8

  3. Dan Bowles says:

    Right answer first time! 🙂

    The key to the prob­lem is that it is pat­tern recog­ni­tion — that is that each tri­an­gle is a dis­tinct event.

  4. david says:

    The cor­rect answer is 3…

    #1 (6–2)*2=8
    #2 (7–5)*3=6
    #3 (7–4)*2=6
    #4 (6–5)*3=

  5. NightLord says:

    I got 8.
    First tri­an­gle total is 18.
    Sec­ond tri­an­gle is 21.
    Third tri­an­gle is 19.
    This, with a skip­ping pat­tern the fourth tri­an­gle should jump to 22.
    Thus, 8 in the last tri­an­gle.

  6. Yomanda says:

    3. fo sho.

  7. zeda says:

    (6*2)-(2*2)= 8
    (7*3)-(5*3)= 6
    (7*2)-(4*2)= 6
    (6*3)-(5*3)= 3

    I muli­ti­plied the top num­ber with the bot­tom right numbe. Then mul­ti­plied the bot­tom two num­bers and sub­tract­ed the two totals. Guess i took the longer route!

  8. yahobahne says:

    i say 7 is the miss­ing num­ber
    pat­tern: 18,21,19,21…
    21 is the con­stant num­ber while the oth­ers decrease by one

  9. siobhan says:

    The answer is 3.


  10. Aaron says:

    I got 8, just because it goes “6, 7, 7, 6” on top, then “8, 6, 6, X” in the tri­an­gle, so the pat­tern would make sense if it were 8.

  11. sudhasini says:

    answer is 3

    IN first train­gle 8/2=4
    add 2 with 4 =6.
    IN sec­ond one
    IN 3rd tri­an­gle
    IN 4th tri­an­gle

  12. Richard says:

    Answer to

    1 3 5 7 9 R

  13. Lmnop says:

    I haven’t checked the answer yet, but I’m going to go ahead and say that it’s 3.

  14. Lmnop says:

    After check­ing the way you were “sup­posed” to get to the answer, I found out I did it the “wrong” way. I did it the same way as zeda. I sup­pose the oth­er way would have been quick­er; oh well.

  15. Truck says:

    I get 2 as (7–5)*3 — 4 = 2

  16. jumbo says:

    cor­rect answer is 3

    In 1st tri­an­gle :6*2–2*2 =inside num­ber

    In 2nd tri­an­gle :7*3–3*5 =inside num­ber
    same for 3rd tri­an­gle
    hence in last tri­an­gle num­ber is 3

  17. Theresa says:

    Wow, this works at least 3 oth­er ways. Oth­er peo­ple men­tioned two already but i found it anoth­er way.. which actu­al­ly some­one wrote too.

    1st — 6*2 — 2*2
    3rd — 7*3 — 3*5 = 3

    Its so fun­ny that it is that open to inter­pre­ta­tion.

  18. steve says:

    1) (6x2)-(2x2)=8
    2) (7x3)-(5x3)=6
    3) (7x2)-(4x2)=6
    4) (6x3)-(5x3)=3!

  19. steve says:

    oops, I guess there­sa already thought of that one.

  20. Nestor Hansen says:

    if you mul­ti­plied the top num­ber by the bot­tom right-hand minus left-hand num­ber is mul­ti­plied by the bot­tom right-hand The solu­ción is the same.

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