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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.

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  2. 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.

  3. 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

  4. 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.

  5. 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=

  6. 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.

  7. Yomanda says:

    3. fo sho.

  8. 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!

  9. 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

  10. siobhan says:

    The answer is 3.


  11. 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.

  12. 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

  13. Richard says:

    Answer to

    1 3 5 7 9 R

  14. Lmnop says:

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

  15. 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.

  16. Zobi says:

    I get 1

  17. Truck says:

    I get 2 as (7-5)*3 – 4 = 2

  18. 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

  19. 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.

  20. steve says:

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

  21. steve says:

    oops, I guess theresa already thought of that one.

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