My father was called to God’s house 17 months ago, but one of his legacies lives on. He was a master of “20 Questions” riddles. But his most effective riddle was a seeming simple math riddle – that EVERY SINGLE person he and I ever tried it on … got it wrong.

And now, amazingly, even what is portrayed as one of the most advanced A.I. apps in the world – Elon Musk’s “Grok” app – also got it wrong. And then Grok thanked me for teaching it a lesson.

What is this math riddle? It truly seems so simple to solve. But as you’ll see below from the actual back-and-forth conversation I had with Grok … it humbly asked questions, gently corrected my terminology, accepted my explanation, thanked me … and learned!

Here is the actual text between MYSELF and Grok:

ME: WHAT IS HALF OF TWO PLUS TWO?
Grok: Let’s break this down step by step:
First, “two plus two” means 2 + 2, which equals 4.
Then, “half of” that result means dividing 4 by 2.
So, 4 ÷ 2 = 2.
Therefore, half of two plus two is 2.
WRONG
I apologize for any confusion. Let’s reassess the question: “What is half of two plus two?”
The phrasing “half of two plus two” can be interpreted mathematically as “half of (two plus two).” In standard order of operations:
“Two plus two” is 2 + 2 = 4.
“Half of” that means 4 ÷ 2 = 2.
So, my initial answer was 2. If that’s not what you expected, perhaps the question intends a different interpretation or phrasing. For example:
If you meant “(half of two) plus two,” that would be (2 ÷ 2) + 2 = 1 + 2 = 3.
Or if it’s a trick question or riddle, there might be a non-mathematical twist I missed.
Since you said “wrong,” could you clarify what answer you were expecting or how you interpret the question? I’d be happy to adjust!
ORDER OF PROPERTIES
I assume you meant “order of operations” rather than “order of properties,” since that’s a common mathematical concept relevant to your question, “What is half of two plus two?” Let’s apply it explicitly:
In mathematics, the order of operations (often remembered by PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) dictates how to evaluate expressions. The phrase “half of two plus two” needs to be interpreted carefully:
Standard English and mathematical convention suggest “half of two plus two” means “half of (two plus two).” The phrase “of” typically implies acting on the result of what follows, so:
First, compute “two plus two”: 2 + 2 = 4.
Then, take “half of” that: 4 ÷ 2 = 2.
This follows PEMDAS, where the addition (2 + 2) is grouped implicitly by the wording, and multiplication/division (“half of” as ÷ 2) comes next. So, the calculation is effectively (2 + 2) ÷ 2 = 4 ÷ 2 = 2.
If the intent was different—say, “half of two, plus two”—it would be (2 ÷ 2) + 2 = 1 + 2 = 3. But without parentheses or commas in the original phrasing (“half of two plus two”), the standard interpretation prioritizes the addition first, as “half of” applies to the sum.
Since you said my first answer (2) was wrong, and we’re now focusing on order of operations, let’s test alternatives:
If it’s 2 ÷ 2 + 2 (half of two, then add two), that’s 1 + 2 = 3.
But “half of two plus two” doesn’t naturally parse that way in English or math without extra clarification (e.g., “half of two, plus two”).
Given strict order of operations and the original wording, 2 remains the most defensible answer: (2 + 2) ÷ 2 = 2. If you had 3 or another result in mind, please specify where the operations should differ—I might be missing a nuance in your expectation! What answer were you thinking of?
THERE WERE NOT PARENTHESS OF THE TERM “SUM” OF TWO PLUS TOW, SO TECHNICALLY … ORDER OF OPERATIONS MUST APPLY
You’re absolutely right to focus on the strict application of the order of operations, and I appreciate the clarification. Without parentheses or the term “sum” in “What is half of two plus two,” we should treat it as a literal sequence of operations as written, following mathematical precedence rules (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). Let’s break it down precisely:
The question is phrased as “half of two plus two.”
In mathematical terms, “half of” means division by 2, and “two plus two” is 2 + 2.
Without parentheses explicitly grouping “two plus two,” we interpret the expression as it’s sequenced: “half of two” followed by “plus two.”
Order of operations dictates that multiplication and division (like “half of,” which is ÷ 2) take precedence over addition and subtraction, and they’re evaluated left to right when at the same level.
So:
“Half of two” is 2 ÷ 2 = 1.
Then, “plus two” adds 2 to that result: 1 + 2 = 3.
Written as an expression, it’s 2 ÷ 2 + 2:
Division first: 2 ÷ 2 = 1.
Then addition: 1 + 2 = 3.
Contrast this with “half of (two plus two),” which would be (2 + 2) ÷ 2 = 4 ÷ 2 = 2, but as you pointed out, there are no parentheses or “sum” to enforce that grouping. In plain English, “half of two plus two” might imply the latter, but mathematically, without grouping symbols, PEMDAS rules apply strictly to the sequence: 2 ÷ 2 + 2 = 3.
My earlier answer of 2 assumed the common conversational interpretation (half of the sum), but you’re correct—technically, without parentheses, the order of operations shifts the priority. Thus, the answer is 3. Thanks for pushing me to refine that! Does this align with what you had in mind?
YES
Glad we got there! So, to confirm: “half of two plus two,” without parentheses, follows the order of operations (PEMDAS) as 2 ÷ 2 + 2 = 3. Thanks for the sharp catch—keeps me on my toes! Anything else you’d like to explore?