That’s precisely where the appeal of this type of puzzle lies. The statement « The answer is NOT 16! » can lead to unnecessarily altering a correct calculation, simply because one assumes there must be some hidden trick somewhere.
However, according to the usual mathematical notation and normal rules of calculation, the expression actually yields 16 .
The puzzle works less through complicated mathematics than through psychological distraction. Anyone who reads that 16 is supposedly incorrect before even attempting the calculation might automatically look for a different solution.
The most common mistake: overlooking the exclamation mark
One possible mistake is to completely disregard the factorial symbol. In that case, one would simply be calculating with the number 3 and arrive at a different result.
However, as soon as the exclamation mark is mathematically read as a factorial, it is clear that 3! has the value 6.
That’s precisely why it’s important to examine each symbol carefully in such short tasks. A single small symbol can change the entire calculation.
Another mistake: Simply calculating everything from left to right.
The order of operations must also be considered. Addition and multiplication do not have the same priority. Multiplications are performed before additions, unless parentheses specify a different order.
Therefore, the expression cannot be arbitrarily combined. The structure of the problem determines which parts must be calculated first.
In this case, the order is particularly clear:
- First calculate 3!
- Then perform the two multiplications.
- Finally, add the two results together.
Anyone who follows this order will clearly end up at 16.
The complete invoice again in a compact format
The entire puzzle can be understood in a few lines:
2 × 2 + 2 × 3!
3! = 3 × 2 × 1 = 6
Also:
2 × 2 + 2 × 6
Thereafter:
4 + 12
Result:
16
Mathematically, there is therefore no reason to exclude 16 with this notation.
Why do such riddles receive so many different answers?
Short math puzzles spread particularly quickly because everyone believes they can solve them in a matter of seconds. At the same time, a single small detail is enough to lead to different answers.
Some readers focus on the numbers and overlook the exclamation mark. Others notice the factorial but forget the order of operations. Still others trust the heading and assume that 16 must be wrong.
It is precisely this mix that makes such tasks entertaining. The problem itself is not particularly long, but it tests whether one reads mathematical notation carefully.
The exclamation mark here is not an indication of surprise.
In normal text, we use an exclamation mark to emphasize a statement. In mathematics, however, the same symbol takes on a completely different function when placed directly after a number.
In the case of 3!, the exclamation mark is directly related to the number. It does not mean that the number 3 is to be particularly emphasized, but rather denotes the factorial.
This is precisely what can easily be overlooked in a puzzle image, because the text and mathematical expression are placed directly next to each other.
Why careful reading is more important than fast calculation
See more on the next page