How to solve 4 variables

Question

I received the below puzzle today (via whatsapp):

We tried to solve this, but we can't solve. We think that this puzzle is wrong. Can this be solved? Or is this a wrong puzzle?

Answer 1

You can write the unknowns like this:

$a$ ; $a-9$
$12-a$ ; $-2-a$

This helps you keep the number of unknowns minimal (just $a$).

Now the horizontal ones are satisfied and so is the 1st vertical.
Then (from the 2nd vertical) you get $(a-9) + (-2-a) = 2$ which can never be true.
So this puzzle has no solution indeed.

Answer 2

Change the minus signs to plus signs. Then, if/when we get a solution, we can convert our entries back to fit the original problem.

Now if we add the numbers on the right, we have the sum of all four entries: $$ (a + b) + (c + d) = 9 + 14 = 23$$

Similarly, if we add the numbers along the bottom, we have a different expression of the sum of the four entries: $$(a + c) + (b + d) = 12 + 2 = 14$$

Obviously, $23 \neq 14$, and the puzzle is ill-posed.

Answer 3

Okay

So A - B = 9; A = 9 + B

C - D = 14; C = 14 + D

A + C = 12; (9+B) + (14+D) = 12; B+D = -11

B + D = 2

So B + D-11 = 2. There are no solutions.

Unless there is some other trick. Do you know where this puzzle came from?

Answer 4

Considering the top two squares as $a$ and $b$, the bottom squares as $c$ and $d$, then $$a = 4.5 \\ b = -4.5 \\ c = 7.5 \\ d = 6.5$$