# #20. Pattern Recognition Brain Teaser — The Empty Triangle

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

The Emp­ty Triangle

Ques­tion:
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!

3

SOLUTION:

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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1. rob on August 20, 2007 at 7:15

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 on August 23, 2007 at 9:40

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
Therefore
(6+5) — (6–3) = 8

3. Dan Bowles on October 17, 2007 at 1:36

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

4. david on October 17, 2007 at 2:05

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

5. NightLord on November 28, 2007 at 2:04

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 on November 29, 2007 at 4:12

3. fo sho.

7. zeda on January 17, 2008 at 10:40

(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 on January 20, 2008 at 9:10

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 on January 24, 2008 at 11:17

6–2=4*2=8
7–5=2*3=6
7–4=3*2=6
6–5=1*3=3

10. Aaron on March 23, 2008 at 10:22

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 on April 8, 2008 at 4:23

IN first train­gle 8/2=4
IN sec­ond one
6/3=2+5=7
IN 3rd triangle
6/2=3+4=7
IN 4th triangle
3/3=1+5=6

12. Richard on May 9, 2008 at 9:13

1 3 5 7 9 R
whelmint

13. Lmnop on June 18, 2008 at 4:41

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

14. Lmnop on June 18, 2008 at 4:44

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. Zobi on October 16, 2008 at 6:21

I get 1

16. Truck on October 16, 2008 at 6:22

I get 2 as (7–5)*3 — 4 = 2

17. jumbo on October 16, 2008 at 7:55

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

18. Theresa on January 30, 2009 at 11:36

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.

19. steve on November 1, 2009 at 11:40

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

20. steve on November 1, 2009 at 11:41

oops, I guess there­sa already thought of that one.

21. Nestor Hansen on September 25, 2017 at 3:22

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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