# One to Nine Puzzle

I got those from a cereal box.
You can use each number 1 to 9 only once.
Operation should match the value in the green box horizonal and vertical

My problem is Operation Order isnt specify in the instructions
But because those puzzles are usually for childrens my guess is precedence is left to right and up down.

Also for puzzle A using normal operator presedence

first row will be
9 - XY = 2 --> XY = 7
and there isnt any combination using 1 to 9 to solve that.
* EDIT * My mistake 1*7 = 7 doh

I could solve B but not A using that order.
You can show your B solution
But the correct answer go for the one finding a solution for A or proving there isnt a solution.

TL;DR. The first puzzle is impossible.

Looking at the first row, you incorrectly claim that there is no XY | X,Y e {1-9}
Actually there is. 1 and 7.

BUT

Given the left column, the only possible solution is 9 x 7 - 5 = 58, which means there can't be a 7 in the first ROW.

Proof: 9 x 6 = 54, and we can't subtract to get 58. 9 x 8 = 72, and we need to subtract 14 to get 58

So, we must assume that the operator precedence is left to right.

This makes the first row 9 - 7 x 1 = 2, which runs afoul of our first column., or 9-8 x2 = 2, Which frees up the seven for the first column, but kills us in the second column, where 8 - X + Y = 8, which implies X = Y, which is impossible.

• Beaten by 17 seconds. Damn :D Nov 20 '14 at 18:09
• Nice to see someone else come to the same conclusion. Nov 20 '14 at 18:11
• You are right didnt saw the 1*7 :\$ Nov 20 '14 at 18:23

Assuming left to right precedence, in the third row we should have 1 in the third column, So:

9 -   *   = 2
*   -   *
+   *   = 39
-   +   +
-   * 1 = 1
=   =   =
58  8   7


Then we have 2 for the last column of first row, and the middle one would get the value of 8:

9 - 8 * 2 = 2
*   -   *
+   *   = 39
-   +   +
-   * 1 = 1
=   =   =
58  8   7


Next step follows:

9 - 8 * 2 = 2
*   -   *
+   * 3 = 39
-   +   +
-   * 1 = 1
=   =   =
58  8   7


Now, in the first column, the only possible values are 7 and 5:

9 - 8 * 2 = 2
*   -   *
7 +   * 3 = 39
-   +   +
5 -   * 1 = 1
=   =   =
58  8   7


Then:

9 - 8 * 2 = 2
*   -   *
7 +   * 3 = 39
-   +   +
5 - 4 * 1 = 1
=   =   =
58  8   7


The remaining cell should be 6. This works for the row, but then the column's result would be 6, not 8. I guess this is a typo.

Solution for B:

9 + 7 + 3 = 19
*   *   *
6 - 2 + 4 = 8
+   -   *
1 * 8 - 5 = 3
=   =   =
55  6   60

• +1 for a good explanation (simple typo 6->8) of how an unsolvable puzzle would end up on a cereal box. Nov 20 '14 at 18:22
• +1 Yes, i also tought was a typo too. But want to give you guys a try :) Nov 20 '14 at 18:30

I don't think A is solvable at all, no matter the order of operations.

• First row: 9-a*b=2

For any order of operations, the only options for a and b are 7 and 1. If you tried using left-to-right order and 9-8*2, then you run into a problem in the middle column where you have 8-c+d=8, which needs a repeated number.

• First column: 9*e-f=58

Since 58 is not a multiple of 9, the order of operation can only be multiplication first. So now we need a multiple of 9 that is more than 58, but less than 68 (since you can only subtract a single digit number to get to 58). The only one is 63, which is 9*7. However, 7 is already taken (first row) and can't be used again.