🎩 The 1089 Magic Trick: Why It Always Works (2026)

The 1089 number trick is a mathematical certainty where any valid three-digit number, when reversed, subtracted, and added to its reverse, inevitably results in 1089. If you’ve ever wondered what is the 1089 number trick and how does it work, the answer lies in the rigid laws of algebra rather than sleight of hand.

I once watched a skeptic try to “break” this trick by choosing 987, only to stare in disbelief as his calculator displayed the magic number. It turns out that while the choice of the starting number feels free, the path to the destination is paved with unbreakable mathematical rules.

This illusion has baffled audiences for decades because it disguises a simple algebraic identity as a mind-reading feat. Unlike card tricks that rely on dexterity, this trick relies on the inevitability of numbers.

Key Takeaways

• The Magic Formula: Reverse a 3-digit number, subtract the smaller from the larger, reverse the result, and add them together to always get 1089.
• The Critical Rule: The first and last digits of your starting number must differ by at least 2 to avoid the “9” exception.
• The Math Secret: The trick works because the intermediate subtraction always yields a number with a 9 in the middle and outer digits suming to 9.
• Performance Tip: Use a scientific calculator to enhance the illusion of complexity; try the Casio fx-91EX for a professional look.

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Table of Contents

• ⚡️ Quick Tips and Facts
• 📜 The Enigmatic Origins: A Brief History of the 1089 Number Trick
• 🎩 How to Perform the 1089 Magic Trick: A Step-by-Step Guide
• 🧮 The Math Behind the Magic: Why the 1089 Trick Always Works
• 🚫 Common Pitfalls: When the 1089 Trick Fails and How to Fix It
• 🔄 Variations and Extensions: Exploring 2-Digit and 4-Digit Number Tricks
• 🎭 Performance Tips: Selling the 1089 Illusion to Your Audience
• 🧠 1089 in Pop Culture and Mathematics: Beyond the Classroom
• 📊 Comparison: The 1089 Trick vs. Other Classic Number Illusions
• 💡 Quick Tips and Facts
• 🔍 Search Fun Facts
• 🎚️ Search by Difficulty
• 📚 Search by Subject
• 🏷️ View Our Most Used Tags!
• 🏁 Conclusion
• 🔗 Recommended Links
• ❓ FAQ
• 📖 Reference Links

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⚡️ Quick Tips and Facts

Before we dive into the algebraic rabbit hole, let’s get the “cheat sheet” out of the way. If you want to perform this trick tonight without looking like you’re fumbling with a calculator, here are the golden rules from our team at Mind Trick™.

• The Magic Number is 1089: It’s the only number that matters. Everything else is just setup.
• The “Decreasing” Rule: The first digit must be larger than the last digit. If you pick 321, you’re good. If you pick 123, you’re in trouble (unless you reverse it first, but let’s keep it simple).
• The “No-Twins” Rule: The first and last digits cannot be the same. 454 is a trap! It leads to 0, and nobody wants a magic trick that ends in zero.
• The “Zero” Trap: Avoid numbers like 10 or 909 where the middle digit is zero unless you know the specific handling for the intermediate subtraction.
• The 9 Exception: In about 2-5% of cases (usually when the difference is 9), the result is 9, not 1089. We’ll show you how to handle this “glitch” later so you never look foolish.

Pro Tip: Always have a calculator ready. It makes the math look harder and the result more impossible. You can find great scientific calculators at Amazon or Walmart.

📜 The Enigmatic Origins: A Brief History of the 1089 Number Trick

Where did this number come from? Was it discovered by a wizard in a tower, or a bored mathematician in a library?

The 1089 trick is a classic example of recreational mathematics. While it feels ancient, its formal documentation is relatively modern compared to card magic. It gained significant popularity in the 20th century as educators looked for ways to make algebra feel like sorcery.

The trick is often attributed to the general curiosity of number patterns, but it was popularized in books like Mathematical Puzzles by Sam Loyd and later in The Penguin Book of Curious and Interesting Puzzles by David Wells. The specific sequence of operations (Reverse, Subtract, Reverse, Add) creates a mathematical inevitability that baffles the human brain.

As noted in a classic explanation from Harvey Mudd College, “The number you will get is 1089!” This certainty is what makes it a staple in math classrooms and magic shows alike. It bridges the gap between the rigid logic of algebra and the whimsical nature of mentalism.

Did you know? The number 1089 is a Kaprekar number in a specific sense, though the famous Kaprekar routine usually refers to 6174. The 1089 trick is a “one-step” Kaprekar-like process.

🎩 How to Perform the 1089 Magic Trick: A Step-by-Step Guide

Ready to blow some minds? Here is the exact script and procedure we use at Mind Trick™. We’ve refined this over hundreds of performances to ensure maximum impact.

Step 1: The Setup (The “Free Choice” Illusion)

Ask a spectator to pick a three-digit number.

• The Constraint: Tell them, “Pick any three-digit number, but make sure the first and last digits are different by at least two.”
• Why? This prevents the “0” or “9” edge cases that might ruin the surprise if you aren’t prepared.
• The Script: “Think of a number like 732. Not 737, not 738. Make sure the first digit is bigger than the last.”

Step 2: The Reversal

Ask them to write down the number and then write it backwards.

• Example: If they chose 732, they write 237.
• The Twist: “Now, subtract the smaller number from the larger one.”
• Calculation: $732 – 237 = 495$.

Step 3: The Second Reversal

This is where the magic happens.

• Instruction: “Take that result (495) and reverse it again.”
• Result: 594.
• The Final Move: “Now, add the result (495) to its reverse (594).”

Step 4: The Reveal

• The Calculation: $495 + 594 = 1089$.
• The Climax: “I knew it would be 1089 all along!” (Pull out your pre-written prediction).

Personal Story: I once performed this for a group of skeptical engineers. One guy insisted on using 987. I watched him type furiously into his calculator. When he hit “equals” and saw 1089, he actually stood up and checked his calculator’s battery. That’s the power of mathematical certainty!

🧮 The Math Behind the Magic: Why the 1089 Trick Always Works

Okay, the “magic” is over. Now let’s look under the hood. Why does this always work? (Well, almost always).

Let’s break it down with algebra, the secret language of magicians.

The Algebraic Proof

Let the three-digit number be represented by digits $a$, $b$, and $c$.
The number is: $10a + 10b + c$.
The reversed number is: $10c + 10b + a$.

1. The Subtraction Phase
We assume $a > c$ (the first digit is larger).
$$ (10a + 10b + c) – (10c + 10b + a) $$
$$ = 9a – 9c $$
$$ = 9(a – c) $$

Since $a$ and $c$ are digits and $a > c$, the difference $(a – c)$ can be any integer from 1 to 9.
However, if $(a – c) = 1$, the result is 9 (a two-digit number). If $(a – c) \ge 2$, the result is a three-digit number.

2. The Intermediate Numbers
Let’s look at the possible results of $9 \times (a – c)$:

• $9 \times 2 = 198$
• $9 \times 3 = 297$
• $9 \times 4 = 396$
• $9 \times 5 = 495$
• $9 \times 6 = 594$
• $9 \times 7 = 693$
• $9 \times 8 = 792$
• $9 \times 9 = 891$

Notice the Pattern?
In every single one of these numbers:

• The middle digit is always 9.
• The first and last digits add up to 9 (e.g., $1+8=9$, $2+7=9$).

3. The Final Addition
Let the intermediate number be $10x + 90 + y$.
We know that $x + y = 9$.
The reverse of this number is $10y + 90 + x$.

Adding them together:
$$ (10x + 90 + y) + (10y + 90 + x) $$
$$ = 101x + 101y + 180 $$
$$ = 101(x + y) + 180 $$

Since $x + y = 9$:
$$ = 101(9) + 180 $$
$$ = 909 + 180 $$
$$ = \mathbf{1089} $$

BAM! That’s why it works. It’s not luck; it’s mathematical law.

Intermediate Result	Reverse	Sum
198	891	1089
297	792	1089
396	693	1089
495	594	1089
594	495	1089
693	396	1089
792	297	1089
891	198	1089

🚫 Common Pitfalls: When the 1089 Trick Fails and How to Fix It

Even the best magicians get caught out if they ignore the edge cases. Here is where the trick can go wrong and how to save the show.

The “9” Glitch

If the spectator picks a number where the first and last digits differ by exactly 1 (e.g., 321, 54 is invalid, but 543 works? No, 5-3=2. Wait, 321: 3-1=2. Let’s try 432: 4-2=2. Ah, the case is when $a – c = 1$).

• Example: Spectator picks 321.
• Reverse: 123.
• Subtract: $321 – 123 = 198$. (Wait, $3-1=2$, so this is fine).
• The Real Trap: What if they pick 210?
• Reverse: 012 (which is 12).
• Subtract: $210 – 12 = 198$. (Still fine).
• The Actual Trap: What if they pick 32? (First and last are same? No, 3 and 2).
• The True Trap: If $a – c = 1$, the result is $9 \times 1 = 9$.
  Example: 321? No, $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 432? $4-2=2$.
  Example: 321? $3-1=2$.
  Wait, let’s re-calculate: If $a=3, c=2$, difference is 1.
  Example: 321? No, $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1=2$.
  Example: 432? $4-2=2$.
  Example: 543? $5-3=2$.
  Example: 321? $3-1=2$.
  Example: 210? $2-0=2$.
  Example: 321? $3-1