This puzzle has been shared millions of times, usually with the boast that “97% of people fail it.” It looks like simple addition, but it is not. The four lines are:
1+4=5
2+5=12
3+6=21
5+8=?
There are two defensible answers, and almost everyone who argues about this puzzle is defending one of them without seeing the other. Let us work through both and see which one actually holds up.
The Trap: Reading “+” as Addition
The first mistake is the obvious one: treating “+” as ordinary addition. Plain addition gives 1+4=5 (correct line one!), then 2+5=7, which is not 12. So the “+” here is not really addition. It stands in for a hidden rule – some operation on the two numbers that happens to equal 5 on line one.
The right question is not “what is 5+8?” It is “what rule turns (1,4) into 5, (2,5) into 12, and (3,6) into 21?”
Step 1: Guess the Rule From Line One
Line one says 1+4=5. Many rules fit a single line, so treat it as a starting hypothesis. One candidate: multiply the two numbers, then add the first number.
1 + (1 x 4) = 1 + 4 = 5
That matches line one. Now the real test: does this rule work on every line, or just the first?
Step 2: Test the Rule on Every Line
A rule only counts if it explains all the given lines. Check it:
- 2 + (2 x 5) = 2 + 10 = 12
- 3 + (3 x 6) = 3 + 18 = 21
Every line checks out. The hidden rule is a + (a x b), which can also be written as a x (b + 1):
- 1 x 5 = 5
- 2 x 6 = 12
- 3 x 7 = 21
Apply it to the last line:
5 + (5 x 8) = 5 + 40 = 45
Answer: 45. This rule uses only the lines actually printed, with no extra assumptions.
Step 3: The Case for 34 (and Why It Is Weaker)
The other popular answer is 34, and it comes from a different reading: add each line’s numbers to a running total.
- 1+4 = 5
- 5 + 2+5 = 12
- 12 + 3+6 = 21
- 21 + 5+8 = 34
This works on the printed lines too – but notice the jump from 3+6 straight to 5+8. The pattern skips 4+7. If the sequence is meant to be consecutive, the missing line is 4+7, which would give 21 + 4+7 = 32, and then 32 + 5+8 = 45. The running-total reading converges to 45 once you fill in the skipped line.
So 34 is only correct if you assume the printed lines are the complete sequence AND that each line builds on the previous one. The 45 answer needs neither assumption.
Verdict: 45
Of the two readings, 45 is the stronger answer because the rule a + (a x b) explains every printed line directly, while 34 requires you to treat the lines as consecutive and silently skip 4+7 – and even then, completing the sequence gives 45 anyway.
Try It Yourself
Once you see the trick, you can solve any puzzle in this family. Pick two numbers, say 6 and 3, and apply the rule: 6 + (6 x 3) = 24. Then test a friend: write “6+3=24” as a new line and watch them squirm.
Enjoyed this? Try these next: If x^x = 49, Then x = ? (Solved Step by Step) and NYT Pips: How to Solve the Domino Logic Puzzle (Strategy Guide).