At first glance, this looks like a very easy subtraction problem.
A professor has **10 pieces of chalk**.
They use **2**.
They lose **1**.
Then something unusual happens.
They take **2 of the remaining pieces** and break each one into **4 separate pieces**.
So the question seems simple:
**How many pieces of chalk are left?**
Most people immediately start subtracting.
10 minus 2.
Minus 1.
Then perhaps another subtraction.
And that's exactly where this little riddle can catch you.
Because the final step isn't about simply removing chalk.
The professor **breaks** the chalk.
And breaking something doesn't make it disappear.
It changes the number of physical pieces.
So before jumping to an answer, let's carefully follow what happened.
## Start With 10 Pieces
The professor begins with:
**10 pieces of chalk.**
Nothing complicated yet.
We have ten separate pieces sitting in their possession.
Then the professor uses two of them.
## Two Pieces Are Used Up
The riddle says the professor **“used 2 up.”**
That means those two pieces are completely consumed.
They're no longer available as pieces of chalk.
So we subtract them:
**10 − 2 = 8**
The professor now has:
**8 pieces.**
So far, this really is just basic subtraction.
But the next clue changes things.
## Then One Piece Is Lost
The professor loses one of the remaining pieces.
Again, that piece is no longer in their possession.
So we subtract one more:
**8 − 1 = 7**
Now there are:
**7 pieces of chalk remaining.**
At this point, many people might be tempted to answer **7**.
After all, two were used and one was lost.
But the riddle isn't finished.
And the next sentence is the part that changes everything.
## Then Two Pieces Are Broken
The professor takes **2 of the remaining 7 pieces**.
They don't use them.
They don't lose them.
They **break them**.
And the riddle gives us another very important detail:
Each piece is broken into **4 pieces**.
That means we're not simply subtracting those two pieces.
We're replacing them with smaller pieces.
Think about it this way.
The professor has:
**7 pieces.**
They take away 2 whole pieces from that group to break them.
That leaves:
**7 − 2 = 5 whole pieces.**
So there are now five pieces that haven't been broken.
But what happened to the two pieces that were broken?
They didn't disappear.
They're still there.
They were simply divided into smaller pieces.
## Each Broken Piece Becomes Four
The first piece is broken into:
**4 pieces.**
The second piece is also broken into:
**4 pieces.**
So together, the two original pieces become:
**4 + 4 = 8 pieces.**
Now we have:
**5 unbroken pieces**
plus
**8 smaller pieces**
And that's where the answer appears.
## Add Everything Together
We have:
**5 original pieces remaining**
and
**8 pieces created by breaking the other two.**
So:
**5 + 8 = 13**
That means the professor now has:
# **13 PIECES OF CHALK** ✏️🧠
And that's the trick.
The number went **up** even though the professor started by losing and using pieces.
## Why Doesn't the Answer Stay at 7?
This is where the wording matters.
If the riddle had said:
**“They threw away 2 of their last ones,”**
then we'd subtract those two.
If it said:
**“They used 2 more,”**
we'd subtract them.
But it says they **broke** them into four pieces each.
Breaking an object doesn't necessarily reduce the number of physical pieces.
It can actually increase the number of separate pieces.
One piece becomes four.
Another piece becomes four.
So two pieces become eight.
That's a very different situation from simply losing two pieces.
## The Trap Is the Word “Broke”
The word **“broke”** is doing all the work in this puzzle.
When people read quickly, they tend to process the story like this:
10 pieces.
Use 2.
Lose 1.
Break 2.
Therefore:
**10 − 2 − 1 − 2 = 5.**
But that calculation treats the broken pieces as if they disappeared.
They didn't.
The two pieces still physically exist.
They've just been divided.
That's why the correct calculation needs another step.
## Let's Do It Slowly
Here's the entire puzzle in numbers.
### Step 1
Start with:
**10**
### Step 2
Use 2:
**10 − 2 = 8**
### Step 3
Lose 1:
**8 − 1 = 7**
### Step 4
Take 2 pieces to break:
**7 − 2 = 5 whole pieces**
### Step 5
Each of those 2 pieces becomes 4:
**2 × 4 = 8 smaller pieces**
### Step 6
Put them together:
**5 + 8 = 13**
So the final answer is:
# **13**
## But Wait… Isn't There Another Way to Think About It?
This is where the riddle gets interesting.
Some people may argue about what exactly counts as a “piece.”
If a piece of chalk is broken into four parts, are all four parts still pieces of chalk?
For this puzzle, the intended answer is clearly **yes**.
The question asks how many **pieces of chalk** are left, and the provided explanation treats each resulting fragment as an individual piece.
Under that interpretation, the answer is 13.
It's a wordplay-and-arithmetic puzzle rather than a scientific measurement problem.
## Why This Riddle Tricks People
The human brain loves shortcuts.
When you see:
**10**
then:
**2 used**
then:
**1 lost**
your brain immediately begins subtracting.
That's exactly what the puzzle wants.
Then it gives you:
**2 broken into 4 each.**
Your brain may still be in subtraction mode.
But now you need to switch from subtraction to multiplication.
That's the key.
The puzzle isn't asking:
**“How many original pieces remain unaltered?”**
It's asking:
**“How many physical pieces exist now?”**
Those are two completely different questions.
## The Five Whole Pieces Are Still There
After the professor chooses two pieces to break, five original pieces remain untouched.
Those five don't change.
So we keep:
**5.**
Then we account for the two broken pieces.
Each becomes four.
So:
**2 × 4 = 8.**
And:
**5 + 8 = 13.**
Nothing disappeared during the breaking process.
The original two pieces simply became eight smaller ones.
## A Simple Example
Imagine you have one cookie.
You break it into four pieces.
Did you destroy the cookie completely?
Not necessarily.
You now have:
**4 pieces of cookie.**
The same principle applies here.
Two pieces of chalk are divided into four pieces each.
So instead of having two pieces, you now have eight pieces.
That's why the final number can be greater than the number you had before the breaking.
## The Most Common Wrong Answers
There are several answers people might give.
### **5**
This comes from subtracting everything:
10 − 2 − 1 − 2 = 5.
The problem is that the broken pieces haven't disappeared.
### **7**
This answer comes from stopping after the professor uses two and loses one.
But it ignores the final event.
### **9**
Some people may subtract the two pieces being broken and then add only four, forgetting that **both** pieces are broken into four.
### **13**
This is the intended answer.
Five untouched pieces plus eight newly separated pieces.
## The Important Difference Between “Used,” “Lost,” and “Broken”
The riddle deliberately uses three different actions.
**Used up** means the chalk is consumed.
**Lost** means the chalk is no longer available.
**Broken** means the chalk changes form but still exists.
That's the entire puzzle.
If you understand those three words, the answer becomes much easier.
The first two actions reduce the number of pieces.
The last action increases the number of separate pieces.
## Why This Is a Great Brain Teaser
The arithmetic itself is extremely simple.
You don't need complicated mathematics.
You just need to pay attention to what happens to each object.
That's why riddles like this are so effective.
They don't test whether you can perform difficult calculations.
They test whether you can avoid making an assumption too quickly.
The moment you read **“broke 2 of their last ones into 4 pieces each,”** you should stop subtracting.
Now you're multiplying.
## Final Calculation
Let's put everything into one equation:
**10 − 2 − 1 − 2 + (2 × 4)**
First:
**10 − 2 = 8**
Then:
**8 − 1 = 7**
Then:
**7 − 2 = 5**
And finally:
**5 + 8 = 13**
Therefore:
# **13 PIECES OF CHALK** ✏️
## Final Thoughts
This riddle is a perfect example of why you shouldn't rush through a question just because the numbers look easy.
The first part encourages you to subtract.
The final part forces you to change your thinking.
The professor starts with 10 pieces.
Two disappear through use.
One disappears because it is lost.
But the next two don't disappear at all.
They are broken into smaller pieces.
And two pieces becoming four each creates **eight separate pieces**.
Five whole pieces remain untouched.
Eight smaller pieces now exist.
Together:
**5 + 8 = 13.**
So if you answered **13**, you caught the trick.
If you answered **5 or 7**, the word **“broke”** probably caught you.
And that's exactly what makes this seemingly simple chalk question such a fun little brain teaser. 🧠✏️
**Did you get 13 on your first try, or did you subtract the broken pieces and get fooled?**
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