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

June 22, 2007//

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!

**ANSWER:
**

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:**

- #21. Good puzzle for the whole brain: The Blind Beggar

Posted in Brain Teasers

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

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

Right answer first time! :)

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

The correct answer is 3…

#1 (6–2)*2=8

#2 (7–5)*3=6

#3 (7–4)*2=6

#4 (6–5)*3=

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.

3. fo sho.

(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!

i say 7 is the missing number

pattern: 18,21,19,21…

21 is the constant number while the others decrease by one

The answer is 3.

6–2=4*2=8

7–5=2*3=6

7–4=3*2=6

6–5=1*3=3

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.

answer is 3

IN first traingle 8/2=4

add 2 with 4 =6.

IN second one

6/3=2+5=7

IN 3rd triangle

6/2=3+4=7

IN 4th triangle

3/3=1+5=6

Answer to

1 3 5 7 9 R

whelmint

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

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.

I get 1

I get 2 as (7–5)*3 — 4 = 2

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

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.

1) (6x2)-(2x2)=8

2) (7x3)-(5x3)=6

3) (7x2)-(4x2)=6

4) (6x3)-(5x3)=3!

oops, I guess theresa already thought of that one.

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.