No way am I going to post the answer here (not like I have it, but I'm positive Google will spoil the fun. Honor system -- if you know the answer, give let's hear it, and show your work.

Here's how you did with last week's pop quiz with the tanks of water.

In other words, there is more than one correct answer

Here's my take on this

1+4; 2+5; 3+6;4+7; 5+8; 6+9; 7+10;8+11... but the last line is given as 8+12=X so maybe there is an aspect to the formula to determine the B in the equation A+Ba=X that people are missingwe'rehard at work.fourvalid answers and six winners.cobrakiller. (Falselife, you didn't show your work, which was Fancy's stipulation.)SAMSONMOLLYoragurney(can't tell who was first). Alternate methodology: Add 1 to the 2nd number and multiply by the 1st. Credit:Dead-Kittens.andrew mann.broizfam.2nd is in base 5: 2+5 5 in base 5 is written as 10 and then there's 2 left over: 10+2=12

3rd is in base 4: 3+6 4 in base 4 is written as 10. There are 2 of them so it's 20 with 1 left over: 20+1=21

If I'm correct then the next one should now be down to base 3: 8+12 3 in base 3 is written as 10. There are 6 3s so that gives 60 with 2 left over: 60+2=62

7+7 = X

Solve for X (hint it is NOT 14)

1x4=4, 4+1=5

2x5=10, 10+2=12

3x6=18, 18+3=21

8x12=96, 96+8=104

here is another question based on that therom if 6x9=42 what is 7+7?

1+4=5 → 14-5=A

2+5=12 → 25-12=B

3+6=21 → 36-21=C

8+12=? → 812-?=D

A=9, B=13, C=15, D=??

Since B-A=2*2, and C-B=2*1, we must have D-C=2*0, so D=C=15

812-?=15 → ?=812-15=797

So the final answer to the puzzle is 797.

By accepting any rule, we can get any answer we like.

1 + (4x1)= 5

2 + (5x2)=12

3 + (6x3)=21

8 + (12x4)=56

not sure why the last numbers jump though from 3 to 8 and 6 to 12 though?

threevalid solutions. Welcome to I-A-B, btw!Hmmm. 41 works, but it means the first line serves only to prime the pump, so to speak. All in all, I think I prefer MeGrendel's solution because it works for every line of numbers. Good job, MeGrendel.

UPDATE: So a couple follow-up thoughts. First, after checking around online, the two solutions presented in this thread are both considered valid and have erupted into a kind of white & gold/blue & black dress contoversy. Second, I'm actually starting to prefer my 41 answer for the following reason. Of the two solutions, it's the only one requiring that the puzzle begin the way it does: 1 + 4 = 5. Why? Because contrary to my original thinking, it isn't there just to prime the pump: It works with no antecedent, thus: 1 + 4 + zero (because there's no preceding line) = 5. It's the only line in the puzzle where the equation makes sense as read because it's the only line with no preceding line. That suggests to me that the creator of the puzzle was using the method that produces the answer 41. I wish I could say I was smart enough to have seen both solutions, and then preferred the 41 on the grounds given above, but that's not the case. 41 was just the answer the popped out at me.

a + b = a x b + a

1 + 4 = 1 x 4 + 1 = 5

2 + 5 = 2 x 5 + 2 = 12

3 + 6 = 3 x 6 + 3 = 21

8 + 12 = 8 x 12 + 8 = 104

a + b = a + b + previous answer

1 + 4 = 1 + 4 + 0 = 5

2 + 5 = 2 + 5 + 5 = 12

3 + 6 = 3 + 6 + 12 = 21

8 + 12 = 8 + 12 + 21 = 41

a + b = a x (b+1)

1 + 4 = 1 x (4 + 1) = 5

2 + 5 = 2 x (5 + 1) = 12

3 + 6 = 3 x (6 + 1) = 21

8 + 12 = 8 x (12 + 1) = 104

Haha, I just realized that the first one and the last one are the same. Of course. Algebra! OK, I'm done.

1+4=5

2+5=7 +5=12

3+6=9 +12=21

8+12=20 +21=41

(1+4) + (2+5) = 12 (second line)

(1+4) + (2+5) + (3+6) = 21 (third line)

(1+4) + (2+5) + (3+6) + (8+12) =

41the answer.I have no idea why it goes 1,2,3, 8... or 5,7,9, 20...but that's a different question :-p

104(1st number x 2nd number) + 1st number

No Google involved, just bored.

Edit: I made the assumption that "8 + 12 + ?" was just another i-am-bored typo that should have been "8 + 12 = ?"

Please let me know if I am a "hotshot".