A 3rd grade math problem: fill in blanks with numbers to obtain a valid equation

Question

Even though this is a 3rd-grade math problem, people found it extremely hard. Any people have a solution, or algorithm is welcome. I'll try make a program base on the algorithm and see if it's correct. And, people are welcome to provide the best solution (least loop, recursion)

Enough said, here's the original: Fill in the blank the number from 1-9 to complete the equation. (probably distinct numbers each blank)

enter image description here

PS: Help me with tags. I'm not sure which tags should I use.

EDIT 1: After a few shortened, here's what I've got:

a + d - f + 12*e + 13*b/c + g*h/j = 87.

So, as you see, the priority does matter.

EDIT 2: Maybe my description is not clear enough, but I think it require to use every number

Like this: an array from [1:9], each fill in the blank remove one component. As Martigan point out, it's like: fill in the blanks using once and only once each number from 1 to 9. Simple math here: There are 9*8*7*6*5*4*3*2 = 362880 possibilitities. (You may correct this simple math if I'm wrong).

And b mod c should = 0 (as only integers appear.)

EDIT 3: I just asked my mom (who's an elementary teacher). She's confirmed that 3rd grade has studied about mathematic priority, so sorry Hagen von Eitzen. Your answer is half right, she'd give you an 7/10.

PS2: People, please share your wisdom and provide the math algorithm.

Sorry for my bad English.

Why not just put a zero in every box except that last (empty) one and make that one $76$? — Gregory Grant, May 18 '15 at 16:45
Even if you did that, it's doesn't equal to the end. I'll edit the question. — Eddie, May 18 '15 at 16:46
You have many many possible solutions. I don't see the point of the problem? Do you want a specific solution? What is the criterai to put forward as a measure of success? — Martigan, May 18 '15 at 16:47
There are nine unknowns, $x_1,\dots,x_{9}$. Here's a possible solution: $x_1=76$, $x_2=x_4=x_5=x_6=x_7=x_8=0$, $x_3=1$, $x_{9}=1$. — Gregory Grant, May 18 '15 at 16:49
$76$ $0$ $1$ $0$ $0$ $0$ $0$ $1$ $1$ is a solution. Grilled by @Gregory Rant — Martigan, May 18 '15 at 16:49
1 -> 9 means 9 unknowns. Only 362880 try (because distinct numbers). But only of them true. — Eddie, May 18 '15 at 16:50
As a general comment, you can reduce the problem by stating all products to 0, and keep only one positive and one negative term ($a$,$f$)... You can do what you want then. — Martigan, May 18 '15 at 16:52
I would like to have an algorithm to this problem, with have the least loop as possible. — Eddie, May 18 '15 at 16:52
Do you want to use once and only once each number from 1 to 9? This would be a different and trickier problem. — Martigan, May 18 '15 at 16:53
Probably that is. It's not that easy to solve as you point earlier. That's why i'm having a headache here. It's 3rd-grade math problem :( dafaq my country is thinking? — Eddie, May 18 '15 at 16:55
@Eddie just wondering, how are you so sure it is a third grade problem? — Quality, May 18 '15 at 17:00

score 3 · Answer 1 · answered May 18 '15 at 16:58

I assume that (as usual in this type of problem) the operations are executed left toright (not by arithemtic priority). Here are the solutions:

[9, 4, 8, 6, 7, 3, 1, 2, 5]: $9+13=22$, $22\times 4=88$, $88:8=11$, $11+6=17$, $17+12=29$, $29\times 7=203$, $203-3=200$, $200-11=189$, $189+1=190$, $190\times 2=380$, $380:5=76$, $76-10=66$.
[9, 7, 2, 8, 4, 3, 6, 1, 5]
[9, 6, 3, 8, 5, 7, 2, 1, 4]
[9, 1, 4, 8, 2, 7, 5, 6, 3]
[9, 5, 3, 8, 1, 2, 7, 6, 4]
[9, 2, 4, 7, 8, 6, 5, 1, 3]
[9, 3, 2, 4, 8, 7, 6, 1, 5]
[9, 3, 2, 7, 6, 5, 8, 1, 4]
[9, 5, 3, 7, 1, 2, 8, 6, 4]
[9, 4, 3, 5, 2, 1, 8, 6, 7]
[9, 3, 2, 6, 1, 7, 5, 8, 4]
[9, 3, 2, 5, 1, 7, 6, 8, 4]
[8, 9, 7, 1, 4, 2, 5, 3, 6]
[7, 9, 8, 5, 6, 2, 4, 1, 3]
[7, 9, 4, 8, 6, 2, 3, 1, 5]
[7, 9, 5, 8, 3, 6, 1, 2, 4]
[2, 9, 4, 3, 8, 6, 7, 1, 5]
[7, 9, 5, 6, 1, 8, 3, 4, 2]
[7, 9, 5, 3, 1, 8, 6, 4, 2]
[1, 9, 7, 5, 2, 8, 6, 4, 3]
[1, 9, 7, 3, 5, 8, 6, 2, 4]
[3, 9, 6, 5, 4, 8, 7, 1, 2]
[6, 9, 3, 1, 4, 8, 5, 2, 7]
[1, 9, 3, 7, 2, 5, 8, 4, 6]
[1, 9, 6, 2, 3, 7, 8, 4, 5]
[4, 9, 3, 2, 6, 7, 8, 1, 5]
[3, 9, 4, 6, 5, 1, 8, 2, 7]
[2, 9, 5, 7, 1, 3, 6, 8, 4]
[2, 9, 5, 6, 1, 3, 7, 8, 4]
[7, 9, 5, 6, 3, 1, 2, 4, 8]
[1, 9, 7, 2, 5, 3, 6, 4, 8]
[8, 6, 9, 7, 5, 3, 1, 2, 4]
[8, 3, 9, 5, 7, 6, 1, 2, 4]
[8, 6, 9, 5, 2, 1, 7, 4, 3]
[8, 5, 9, 3, 6, 4, 7, 1, 2]
[8, 1, 9, 3, 4, 2, 7, 6, 5]
[8, 6, 9, 3, 5, 2, 1, 4, 7]
[8, 5, 9, 1, 4, 2, 3, 6, 7]
[5, 4, 9, 1, 8, 7, 2, 3, 6]
[5, 4, 9, 1, 6, 8, 7, 2, 3]
[5, 4, 9, 3, 7, 6, 8, 1, 2]
[5, 1, 9, 3, 7, 2, 8, 4, 6]
[5, 6, 9, 7, 1, 4, 3, 8, 2]
[5, 4, 9, 7, 1, 3, 6, 8, 2]
[5, 6, 9, 3, 1, 4, 7, 8, 2]
[5, 4, 9, 6, 1, 3, 7, 8, 2]
[5, 1, 9, 2, 3, 6, 7, 8, 4]
[5, 4, 9, 1, 3, 2, 7, 8, 6]
[5, 1, 9, 2, 4, 3, 7, 8, 6]
[7, 3, 9, 4, 5, 2, 1, 6, 8]
[5, 7, 9, 1, 6, 2, 3, 4, 8]
[2, 6, 9, 1, 7, 3, 5, 4, 8]
[8, 1, 7, 9, 2, 4, 5, 6, 3]
[8, 4, 3, 9, 5, 7, 1, 2, 6]
[8, 1, 3, 9, 5, 2, 6, 4, 7]
[2, 8, 4, 9, 1, 7, 5, 6, 3]
[5, 8, 6, 9, 1, 3, 7, 4, 2]
[7, 6, 8, 9, 2, 5, 1, 4, 3]
[5, 2, 4, 9, 8, 7, 6, 1, 3]
[3, 1, 4, 9, 8, 6, 7, 2, 5]
[7, 1, 3, 9, 6, 8, 5, 2, 4]
[7, 1, 4, 9, 2, 8, 5, 6, 3]
[5, 7, 6, 9, 4, 8, 3, 1, 2]
[1, 7, 6, 9, 3, 8, 2, 4, 5]
[5, 1, 6, 9, 7, 8, 3, 2, 4]
[5, 4, 1, 9, 3, 8, 6, 2, 7]
[4, 6, 3, 9, 7, 2, 8, 1, 5]
[5, 1, 3, 9, 6, 7, 8, 2, 4]
[5, 4, 3, 9, 6, 1, 8, 2, 7]
[7, 3, 6, 9, 1, 5, 4, 8, 2]
[7, 3, 4, 9, 2, 5, 1, 8, 6]
[2, 7, 6, 9, 1, 4, 5, 8, 3]
[2, 6, 3, 9, 1, 7, 5, 8, 4]
[5, 3, 2, 9, 1, 6, 7, 8, 4]
[7, 1, 3, 9, 6, 5, 2, 4, 8]
[7, 3, 1, 9, 2, 5, 6, 4, 8]
[8, 1, 7, 3, 9, 5, 6, 2, 4]
[8, 4, 7, 3, 9, 5, 1, 2, 6]
[8, 4, 6, 5, 9, 3, 1, 2, 7]
[7, 4, 8, 5, 9, 6, 2, 1, 3]
[7, 2, 8, 1, 9, 4, 5, 3, 6]
[3, 4, 8, 7, 9, 5, 1, 2, 6]
[7, 2, 6, 8, 9, 5, 4, 1, 3]
[7, 1, 3, 8, 9, 5, 4, 2, 6]
[3, 6, 4, 8, 9, 7, 2, 1, 5]
[3, 1, 6, 8, 9, 7, 4, 2, 5]
[7, 6, 4, 2, 9, 8, 3, 1, 5]
[3, 7, 6, 5, 9, 8, 2, 1, 4]
[1, 5, 7, 4, 9, 3, 8, 2, 6]
[5, 1, 6, 3, 9, 7, 8, 2, 4]
[3, 2, 6, 1, 9, 7, 5, 4, 8]
[2, 1, 5, 3, 9, 6, 7, 4, 8]
[1, 8, 6, 7, 3, 9, 2, 4, 5]
[6, 8, 4, 5, 3, 9, 7, 1, 2]
[7, 5, 8, 4, 2, 9, 1, 6, 3]
[7, 2, 5, 1, 8, 9, 4, 3, 6]
[1, 2, 7, 5, 8, 9, 4, 3, 6]
[3, 5, 2, 7, 8, 9, 4, 1, 6]
[1, 4, 7, 5, 2, 9, 8, 6, 3]
[1, 4, 3, 7, 2, 9, 8, 6, 5]
[2, 1, 5, 3, 7, 9, 8, 4, 6]
[2, 7, 3, 6, 1, 9, 5, 8, 4]
[2, 7, 3, 5, 1, 9, 6, 8, 4]
[3, 7, 2, 5, 1, 9, 4, 8, 6]
[3, 7, 2, 4, 1, 9, 5, 8, 6]
[1, 4, 7, 5, 3, 9, 2, 8, 6]
[6, 3, 4, 7, 2, 9, 1, 8, 5]
[4, 1, 6, 7, 3, 9, 2, 8, 5]
[5, 1, 6, 2, 3, 9, 7, 8, 4]
[2, 5, 6, 4, 3, 9, 1, 8, 7]
[6, 2, 1, 5, 3, 9, 7, 4, 8]
[8, 1, 7, 5, 6, 4, 9, 2, 3]
[5, 8, 6, 7, 1, 3, 9, 4, 2]
[2, 8, 4, 5, 1, 7, 9, 6, 3]
[1, 7, 8, 6, 4, 5, 9, 2, 3]
[3, 6, 8, 7, 5, 1, 9, 2, 4]
[1, 6, 7, 8, 2, 5, 9, 4, 3]
[2, 1, 5, 8, 6, 3, 9, 4, 7]
[2, 1, 6, 3, 8, 5, 9, 4, 7]
[2, 6, 5, 4, 7, 8, 9, 1, 3]
[7, 3, 6, 4, 1, 5, 9, 8, 2]
[7, 2, 5, 1, 3, 4, 9, 8, 6]
[2, 7, 6, 5, 1, 4, 9, 8, 3]
[1, 3, 7, 5, 2, 6, 9, 8, 4]
[1, 2, 7, 5, 3, 4, 9, 8, 6]
[5, 3, 2, 7, 1, 6, 9, 8, 4]
[2, 6, 3, 5, 1, 7, 9, 8, 4]
[5, 2, 4, 1, 3, 7, 9, 8, 6]
[3, 5, 4, 1, 2, 7, 9, 8, 6]
[4, 5, 1, 7, 3, 6, 9, 2, 8]
[7, 4, 6, 8, 1, 2, 5, 9, 3]
[7, 4, 6, 5, 1, 2, 8, 9, 3]
[8, 7, 3, 1, 2, 4, 5, 6, 9]
[8, 2, 1, 7, 3, 6, 5, 4, 9]
[8, 2, 1, 6, 3, 5, 7, 4, 9]
[1, 8, 7, 2, 6, 3, 5, 4, 9]
[1, 8, 4, 7, 5, 2, 6, 3, 9]
[5, 8, 3, 1, 2, 4, 7, 6, 9]
[3, 7, 8, 5, 4, 1, 2, 6, 9]
[7, 1, 2, 8, 6, 3, 5, 4, 9]
[7, 2, 1, 8, 4, 6, 5, 3, 9]
[1, 4, 2, 8, 5, 7, 6, 3, 9]
[3, 1, 4, 8, 5, 2, 7, 6, 9]
[5, 7, 4, 1, 8, 6, 3, 2, 9]
[2, 1, 3, 6, 8, 7, 5, 4, 9]
[7, 1, 2, 4, 5, 8, 3, 6, 9]
[4, 6, 1, 7, 2, 8, 5, 3, 9]
[1, 2, 4, 7, 5, 8, 3, 6, 9]
[2, 3, 5, 6, 7, 8, 1, 4, 9]
[4, 6, 1, 5, 2, 7, 8, 3, 9]
[2, 7, 6, 4, 3, 5, 1, 8, 9]
[2, 1, 6, 4, 5, 3, 7, 8, 9]

I've just read your answer more closely. Probably you're right, it's not using arithmetic priority. But what if they does? Because grouping using priority reduce the solutions. — Eddie, May 18 '15 at 17:08
@HagenvonEitzen: A commenter on this Huffingtonpost article also arrived at the total of 152 solutions. Apparently, the puzzle was created by Tan Phuong of Vietnam. — Tito Piezas III, May 21 '15 at 03:46
@TitoPiezasIII Look at my answer. There are only 20 solutions. probably the other commenter was wrong, or didn't use mathematic priority. Or my algorithm is not correct? Can you check it at stackOverflow? — Eddie, May 21 '15 at 04:35
@Eddie: More accurately, if you use one assumption, you get 152 solutions. If you use another, you have just 20 solutions. It depends on how the problem was originally stated. — Tito Piezas III, May 21 '15 at 04:44

score 2 · Answer 2 · answered May 21 '15 at 20:06

There is 1 equation and 9 unknowns, the problem is we have an underdetermined system: http://en.wikipedia.org/wiki/Underdetermined_system.

The only relationship we know (in the typical phrasing of the question) is that they all belong to the set [1...9] and are mutually exclusive. While all solutions can be found using brute force (with a program), I don't believe there is a mathematical way to prove or derive the existence of any solutions since the placement of any number impacts the choices for the remaining numbers and the information is too limited. We know without brute forcing that the system has at most a limited number of solutions. We know from running programs (only after the fact) that the puzzle is consistent and has solutions.

a + d - f + 12*e + 13*b/c + g*h/j = 87

The values of a and d are interchangeable, as are g and h. It does not help us with the problem, but it does show that if at least 1 solution exists, then more than 1 solution must exist; specifically, if you find 1 it has 4 variants since some of the math is commutative.

So, to summarize, you're saying that there are no mathematical solution to this problem? Brute force is the only way? — Eddie, May 22 '15 at 04:39

score 1 · Answer 3 · edited May 23 '17 at 12:39

I ask StackOverflow for a programmatic solution, turn out having 20 answer:

2015-05-20 01:44:23.568 Math[29526:3757225] a=3 b=2 c=1 d=5 e=4 f=7 g=8 h=9 i=6
2015-05-20 01:44:23.569 Math[29526:3757225] a=3 b=2 c=1 d=5 e=4 f=7 g=9 h=8 i=6
2015-05-20 01:44:24.074 Math[29526:3757225] a=5 b=2 c=1 d=3 e=4 f=7 g=8 h=9 i=6
2015-05-20 01:44:24.075 Math[29526:3757225] a=5 b=2 c=1 d=3 e=4 f=7 g=9 h=8 i=6
2015-05-20 01:44:24.127 Math[29526:3757225] a=5 b=3 c=1 d=7 e=2 f=6 g=8 h=9 i=4
2015-05-20 01:44:24.127 Math[29526:3757225] a=5 b=3 c=1 d=7 e=2 f=6 g=9 h=8 i=4
2015-05-20 01:44:24.162 Math[29526:3757225] a=5 b=4 c=1 d=9 e=2 f=7 g=3 h=8 i=6
2015-05-20 01:44:24.163 Math[29526:3757225] a=5 b=4 c=1 d=9 e=2 f=7 g=8 h=3 i=6
2015-05-20 01:44:24.290 Math[29526:3757225] a=5 b=9 c=3 d=6 e=2 f=1 g=7 h=8 i=4
2015-05-20 01:44:24.290 Math[29526:3757225] a=5 b=9 c=3 d=6 e=2 f=1 g=8 h=7 i=4
2015-05-20 01:44:24.381 Math[29526:3757225] a=6 b=3 c=1 d=9 e=2 f=5 g=7 h=8 i=4
2015-05-20 01:44:24.381 Math[29526:3757225] a=6 b=3 c=1 d=9 e=2 f=5 g=8 h=7 i=4
2015-05-20 01:44:24.548 Math[29526:3757225] a=6 b=9 c=3 d=5 e=2 f=1 g=7 h=8 i=4
2015-05-20 01:44:24.548 Math[29526:3757225] a=6 b=9 c=3 d=5 e=2 f=1 g=8 h=7 i=4
2015-05-20 01:44:24.630 Math[29526:3757225] a=7 b=3 c=1 d=5 e=2 f=6 g=8 h=9 i=4
2015-05-20 01:44:24.630 Math[29526:3757225] a=7 b=3 c=1 d=5 e=2 f=6 g=9 h=8 i=4
2015-05-20 01:44:25.115 Math[29526:3757225] a=9 b=3 c=1 d=6 e=2 f=5 g=7 h=8 i=4
2015-05-20 01:44:25.115 Math[29526:3757225] a=9 b=3 c=1 d=6 e=2 f=5 g=8 h=7 i=4
2015-05-20 01:44:25.143 Math[29526:3757225] a=9 b=4 c=1 d=5 e=2 f=7 g=3 h=8 i=6
2015-05-20 01:44:25.143 Math[29526:3757225] a=9 b=4 c=1 d=5 e=2 f=7 g=8 h=3 i=6
2015-05-20 01:44:25.294 Math[29526:3757225] Result: 20 correct / 362880 total

Not sure how it will look like as a mathematic problem.

that's incorrect, there are 136 solutions ... someone clearly didn't pay attention to floating operations ... here is a python script - https://repl.it/oxA/7 — scibuff, May 21 '15 at 13:55

score 1 · Accepted Answer · answered May 25 '15 at 00:09

There are 136 solutions for this:

126478359 1 2 6 4 7 8 3 5 9 66

126478539 1 2 6 4 7 8 5 3 9 66

132458796 1 3 2 4 5 8 7 9 6 66

132458976 1 3 2 4 5 8 9 7 6 66

132956478 1 3 2 9 5 6 4 7 8 66

132956748 1 3 2 9 5 6 7 4 8 66

134765298 1 3 4 7 6 5 2 9 8 66

134765928 1 3 4 7 6 5 9 2 8 66

136279458 1 3 6 2 7 9 4 5 8 66

136279548 1 3 6 2 7 9 5 4 8 66

139478256 1 3 9 4 7 8 2 5 6 66

139478526 1 3 9 4 7 8 5 2 6 66

148279356 1 4 8 2 7 9 3 5 6 66

148279536 1 4 8 2 7 9 5 3 6 66

152348796 1 5 2 3 4 8 7 9 6 66

152348976 1 5 2 3 4 8 9 7 6 66

152847396 1 5 2 8 4 7 3 9 6 66

152847936 1 5 2 8 4 7 9 3 6 66

153942786 1 5 3 9 4 2 7 8 6 66

153942876 1 5 3 9 4 2 8 7 6 66

183745269 1 8 3 7 4 5 2 6 9 66

183745629 1 8 3 7 4 5 6 2 9 66

196458372 1 9 6 4 5 8 3 7 2 66

196458732 1 9 6 4 5 8 7 3 2 66

196752348 1 9 6 7 5 2 3 4 8 66

196752438 1 9 6 7 5 2 4 3 8 66

214379568 2 1 4 3 7 9 5 6 8 66

214379658 2 1 4 3 7 9 6 5 8 66

236179458 2 3 6 1 7 9 4 5 8 66

236179548 2 3 6 1 7 9 5 4 8 66

248179356 2 4 8 1 7 9 3 5 6 66

248179536 2 4 8 1 7 9 5 3 6 66

269851473 2 6 9 8 5 1 4 7 3 66

269851743 2 6 9 8 5 1 7 4 3 66

286941573 2 8 6 9 4 1 5 7 3 66

286941753 2 8 6 9 4 1 7 5 3 66

296351478 2 9 6 3 5 1 4 7 8 66

296351748 2 9 6 3 5 1 7 4 8 66

314279568 3 1 4 2 7 9 5 6 8 66

314279658 3 1 4 2 7 9 6 5 8 66

321547896 3 2 1 5 4 7 8 9 6 66

321547986 3 2 1 5 4 7 9 8 6 66

324851796 3 2 4 8 5 1 7 9 6 66

324851976 3 2 4 8 5 1 9 7 6 66

328651794 3 2 8 6 5 1 7 9 4 66

328651974 3 2 8 6 5 1 9 7 4 66

352148796 3 5 2 1 4 8 7 9 6 66

352148976 3 5 2 1 4 8 9 7 6 66

364958172 3 6 4 9 5 8 1 7 2 66

364958712 3 6 4 9 5 8 7 1 2 66

392815674 3 9 2 8 1 5 6 7 4 66

392815764 3 9 2 8 1 5 7 6 4 66

396251478 3 9 6 2 5 1 4 7 8 66

396251748 3 9 6 2 5 1 7 4 8 66

426178359 4 2 6 1 7 8 3 5 9 66

426178539 4 2 6 1 7 8 5 3 9 66

432158796 4 3 2 1 5 8 7 9 6 66

432158976 4 3 2 1 5 8 9 7 6 66

439178256 4 3 9 1 7 8 2 5 6 66

439178526 4 3 9 1 7 8 5 2 6 66

496158372 4 9 6 1 5 8 3 7 2 66

496158732 4 9 6 1 5 8 7 3 2 66

512967348 5 1 2 9 6 7 3 4 8 66

512967438 5 1 2 9 6 7 4 3 8 66

521347896 5 2 1 3 4 7 8 9 6 66

521347986 5 2 1 3 4 7 9 8 6 66

531726894 5 3 1 7 2 6 8 9 4 66

531726984 5 3 1 7 2 6 9 8 4 66

541927386 5 4 1 9 2 7 3 8 6 66

541927836 5 4 1 9 2 7 8 3 6 66

548967132 5 4 8 9 6 7 1 3 2 66

548967312 5 4 8 9 6 7 3 1 2 66

572839164 5 7 2 8 3 9 1 6 4 66

572839614 5 7 2 8 3 9 6 1 4 66

593621784 5 9 3 6 2 1 7 8 4 66

593621874 5 9 3 6 2 1 8 7 4 66

628351794 6 2 8 3 5 1 7 9 4 66

628351974 6 2 8 3 5 1 9 7 4 66

631925784 6 3 1 9 2 5 7 8 4 66

631925874 6 3 1 9 2 5 8 7 4 66

693521784 6 9 3 5 2 1 7 8 4 66

693521874 6 9 3 5 2 1 8 7 4 66

714965238 7 1 4 9 6 5 2 3 8 66

714965328 7 1 4 9 6 5 3 2 8 66

728965134 7 2 8 9 6 5 1 3 4 66

728965314 7 2 8 9 6 5 3 1 4 66

731526894 7 3 1 5 2 6 8 9 4 66

731526984 7 3 1 5 2 6 9 8 4 66

732859164 7 3 2 8 5 9 1 6 4 66

732859614 7 3 2 8 5 9 6 1 4 66

734165298 7 3 4 1 6 5 2 9 8 66

734165928 7 3 4 1 6 5 9 2 8 66

752849136 7 5 2 8 4 9 1 3 6 66

752849316 7 5 2 8 4 9 3 1 6 66

764859132 7 6 4 8 5 9 1 3 2 66

764859312 7 6 4 8 5 9 3 1 2 66

783145269 7 8 3 1 4 5 2 6 9 66

783145629 7 8 3 1 4 5 6 2 9 66

796152348 7 9 6 1 5 2 3 4 8 66

796152438 7 9 6 1 5 2 4 3 8 66

824351796 8 2 4 3 5 1 7 9 6 66

824351976 8 2 4 3 5 1 9 7 6 66

832759164 8 3 2 7 5 9 1 6 4 66

832759614 8 3 2 7 5 9 6 1 4 66

852147396 8 5 2 1 4 7 3 9 6 66

852147936 8 5 2 1 4 7 9 3 6 66

852749136 8 5 2 7 4 9 1 3 6 66

852749316 8 5 2 7 4 9 3 1 6 66

864759132 8 6 4 7 5 9 1 3 2 66

864759312 8 6 4 7 5 9 3 1 2 66

869251473 8 6 9 2 5 1 4 7 3 66

869251743 8 6 9 2 5 1 7 4 3 66

872539164 8 7 2 5 3 9 1 6 4 66

872539614 8 7 2 5 3 9 6 1 4 66

892315674 8 9 2 3 1 5 6 7 4 66

892315764 8 9 2 3 1 5 7 6 4 66

912567348 9 1 2 5 6 7 3 4 8 66

912567438 9 1 2 5 6 7 4 3 8 66

914765238 9 1 4 7 6 5 2 3 8 66

914765328 9 1 4 7 6 5 3 2 8 66

928765134 9 2 8 7 6 5 1 3 4 66

928765314 9 2 8 7 6 5 3 1 4 66

931625784 9 3 1 6 2 5 7 8 4 66

931625874 9 3 1 6 2 5 8 7 4 66

932156478 9 3 2 1 5 6 4 7 8 66

932156748 9 3 2 1 5 6 7 4 8 66

941527386 9 4 1 5 2 7 3 8 6 66

941527836 9 4 1 5 2 7 8 3 6 66

948567132 9 4 8 5 6 7 1 3 2 66

948567312 9 4 8 5 6 7 3 1 2 66

953142786 9 5 3 1 4 2 7 8 6 66

953142876 9 5 3 1 4 2 8 7 6 66

964358172 9 6 4 3 5 8 1 7 2 66

964358712 9 6 4 3 5 8 7 1 2 66

986241573 9 8 6 2 4 1 5 7 3 66

986241753 9 8 6 2 4 1 7 5 3 66

I used c++ and Excel to solve it.

Check the solution here:

https://github.com/jpruiz114/cpp-tests/tree/master/DevCppTest02

MAAAANNNN, where do you from? How did you extract all the information and write a complete documentation of this math problem? You're my idol! — Eddie, Aug 24 '15 at 09:39
Hey Eddie, from the US, based in South America. There's a document for this, is here: http://issuu.com/jpruiz114/docs/brute_force_solution_for_vietnamese
Feel free to touch base with me via email. — jpruiz114, Aug 24 '15 at 16:25

A 3rd grade math problem: fill in blanks with numbers to obtain a valid equation

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