# What is the solution of the last operation?

Each symbol represents a number between 0 and 9. You need found the number which is the solution to the last operation. The two triangles in the first operation and the triangle and the rectangle of the third operation represent a number of two digits, not a multiplication operation. So, which is the number that corresponds to the last operation?

• to the downvoter, I'm new in this site, if you can tell me why you vote down, I can improve my next question, thanks – Adrian Cid Almaguer May 3 '15 at 19:34

Let G, R, Y, B denote the digits corresponding to the four shapes in the order they appear (green star, red octagon, yellow triangle, blue rectangle).

In the first equation,

two 1-digit numbers sum to YY, so Y=1 (22 is too large).

In the second equation we learn B=R+1.

Now the third equation is

1B-R = 1(R+1)-R = 11,

11, or two yellow triangles.

• your answer is good, but I can wait some time to see others answers? I make this question because I new in this site – Adrian Cid Almaguer May 3 '15 at 17:18
• Sure you can wait :-) The usual practice here is to accept the first correct and explained answer (assuming it's not really crappy), but this question is an edge case because leoll2 answered first but I was the first to include explanation. – Rand al'Thor May 3 '15 at 17:21

11 (triangle-triangle)

Since star and octagon are two different numbers between 1 and 9, their sum is between 1 and 17. Triangle-triangle means a two digits number, so it must be 11.
Then, we have these valid pairs for Star + Octagon: (2,9),(3,8),(4,7),(5,6),(6,5),(7,4),(8,3),(9,2). Octagon + 1 returns a single digit number, so we can exclude (2,9). Also we can exclude (6,5) because rectangle would be the same of octagon.

Now, if you suppose (3,8), the third equation becomes $19-8=11$.
As well, if you suppose (4,7), it becomes $18-7=11$
If you suppose (5,6), it becomes $17-6=11$
If you suppose (7,4), it becomes $15-4=11$
If you suppose (8,3), it becomes $14-3=11$
If you suppose (9,2), it becomes $13-2=11$

Generally, if you suppose ($11-x,x$) the third equation becomes $(10+1+x)-x=11$

• You got the answer first, but I was first with the explanation! :-) – Rand al'Thor May 3 '15 at 16:47
• @randal'thor very funny ;-) – Adrian Cid Almaguer May 3 '15 at 16:47
• @randal'thor Yeah, I agree with that! – leoll2 May 3 '15 at 16:49
• God dangit why do people have to beat me!!! – awesomepi May 3 '15 at 16:52

Since two integers from 0 to 9 can not add up to a number higher than 18, the triangle is 1. If you substitute the rectangles value into the third equation, the octagon cancels out and becomes...

2 triangles or 11

• You came a few minutes too late to this party! ;-) – Rand al'Thor May 3 '15 at 16:53
• @randalthor ... 3 minutes – awesomepi May 3 '15 at 16:54
• @randal'thor I just signed up on this site and now I'm enjoying it, I have to go more often around here – Adrian Cid Almaguer May 3 '15 at 16:56
• @awesomepi Too many fast people here even on a Sunday afternoon... – Rand al'Thor May 3 '15 at 16:56
• @AdrianCidAlmaguer Yeah, it's a really fun site! I hope you participate more here :-) – Rand al'Thor May 3 '15 at 16:57

Answer: green star+ red octagon+ yellow triangle

Green star = g Yellow triangle = y Red octagon = r

y.y= g+r b=r+y yb-r=

y(r+y)-r =yr+yy-r =yy+r(y-1) =g+r+r(y-1) =g+r(1+y-1) = g+r+y