Can You Determine the Rule in this “Intelligence Test”?

Good luck!

This puzzle went viral on Facebook and was shared over 3 million times. It is supposed to test your intelligence by providing you with a list of equations that seem untrue on the surface, but every single one follows an unidentified rule.

Once you have identified the rule that all of the equations follow, fill in the numbers for the equation at the bottom.

Make sure you give it a try before checking out the solutions. Yes, I said solutions. There is more than one.

Solution:

You may have noticed that the sum of the two digits makes up the last digit in the answer. For example:

6 + 4 = 210	6 + 4 = 10
9 + 2 = 711	9 + 2 = 11
8 + 5 = 313	8 + 5 = 13
5 + 2 = 37	5 + 2 = 7
7 + 6 = 113	7 + 6 = 13
9 + 8 = 117	9 + 8 = 17
10 + 6 = 416	10 + 6 = 16
15 + 3 = 1218	15 + 3 = 18

Also, the difference between the two digits makes up the first digit in the answer.

6 + 4 = 210	6  -4 = 2
9 + 2 = 711	9 - 2 = 7
8 + 5 = 313	8 - 5 = 3
5 + 2 = 37	5 - 2 = 3
7 + 6 = 113	7 - 6 = 1
9 + 8 = 117	9 - 8 = 1
10 + 6 = 416	10 - 6 = 4
15 + 3 = 1218	15 - 3 = 12

This gives us a general equation of: (x + y) = (x - y) | (x + y)

So, what is ? + ? = 123?

The first solution is the more obvious one.

x + y = 23

Luckily, we have two equations to solve for two variables. Let’s solve for x. Rearranging the last two equations, we know y = x - 1 and y = 23 - x. To solve for x, we can replace y in the equation y = 23 - x, with x - 1. This gives:

x = 12

Since we know x - y = 1, then

y= 11

Therefore the equation is: 12 + 11 = 123

But there is one more solution! This time, we can assume:

x + y = 3

Following the same method as above, we can solve for x.

x = 7.5

Therefore,

y = -4.5

And our final solution in this scenario is 7.5 + (-4.5) = 123.

h/t: Curiosity