While I had no interest in teaching math in classrooms full of unruly students, I have taken an unexpected delight in completing online puzzles when and where I find them. The puzzles and riddles surface, and there are plenty of people out there who take pride in their ability to see patterns and solve difficult math problems.

To that aim, we decided to put our dear readers’ minds to the test with a bran-teasing topic that has left many people scratching their heads on the internet.

If 1+4=5, 2+5=12, and , then what is the value of 5+8?

Perhaps it’s easier if you see it written out as follows:

1+4=5
2+5=12
3+6=21
5+8=?

If you’ve had a go at the problem yourself and want to see if you’ve got it right (or if, like me, you were ultimately left so frustrated that you simply have to be given the answer) see below for five different ways the problem can be tackled.

Solution one

1 + 4 = 5
2 + 5 = 2 + 2(5) = 12
3 + 6 = 3 + 3(6) = 21
5 + 8 = 5 + 5(8) = 45
ALGORITHM: A + A(B) = C
ANSWER = 45

Solution two

1 + 4 = 1 + 4 + (0) = 5
2 + 5 = 2 + 5 + (5) = 12
3 + 6 = 3 + 6 + (12) = 21
5 + 8 = 5 + 8 + (21) = 34
ALGORITHM: A + B + C’ = C, where C’ is the previous answer
ANSWER = 34

Solution Three

1 + 4 = 5 = 5
2 + 5 = (5 + 2) + (5) = 12
3 + 6 = (7 + 2) + (12) = 21
5 + 8 = (9 + 2) + (21) = 32
ALGORITHM: for {X=5, C = X + C’ , X = X+2 };, where C’ is the previous answer. A and B not used in equation,
ANSWER = 32

Solution Four

1 + 4 = 5
2 + 5 = 7 (base 5) =12
3 + 6 = 9 (base 4) = 21
5 + 8 = 13 (base 3) = 111
ALGORITHM: for {X=6, C = (A + B)^(10 -> X), X -1} (First answer in Base6, then Base 5, then 4, etc…)
ANSWER = 111

Solution Five

1 + 4 = 5
2 + 5 = 7 (base 5) =12
3 + 6 = 9 (base 4) = 21
4 + 7 = 11 (base 3) = 102
5 + 8 = 13 (base 2) (aka binary) = 1101
ALGORITHM: for {X=6, C = (A + B)^(10 -> X), X -1} (First answer in Base6, then
Base 5, then 4, etc…including “missing” numbers
ANSWER = 1101