Let's solve the cryptarithm "NO + GUN + NO = HUNT."

In this cryptarithm:
- Each letter represents a unique digit.
- The sum of "NO + GUN + NO" must equal the number represented by "HUNT."

We have the equation:
\[
NO + GUN + NO = HUNT
\]
which simplifies to:
\[
2 \times NO + GUN = HUNT
\]

### Step 1: Assign variables for the letters
Let:
- N = \( n \)
- O = \( o \)
- G = \( g \)
- U = \( u \)
- H = \( h \)
- T = \( t \)

So, the numbers look like:
\[
NO = 10n + o
\]
\[
GUN = 100g + 10u + n
\]
\[
HUNT = 1000h + 100u + 10n + t
\]

### Step 2: Set up the equation
Now plug these expressions into the main equation:
\[
2(10n + o) + (100g + 10u + n) = 1000h + 100u + 10n + t
\]

This simplifies to:
\[
20n + 2o + 100g + 10u + n = 1000h + 100u + 10n + t
\]
\[
21n + 2o + 100g + 10u = 1000h + 100u + 10n + t
\]
Now we can simplify further and solve the system by testing possible digit values for each letter, while ensuring that no two letters share the same digit.

### Step 3: Trial and error method
We can now try different values for the variables.

Let me calculate this step by step.There are several valid solutions to the cryptarithm "NO + GUN + NO = HUNT." Here are a few of the solutions:

1. \( N = 1, O = 2, G = 8, U = 9, H = 0, T = 5 \)
2. \( N = 1, O = 3, G = 8, U = 9, H = 0, T = 7 \)
3. \( N = 1, O = 6, G = 7, U = 8, H = 0, T = 3 \)
4. \( N = 2, O = 1, G = 7, U = 8, H = 0, T = 4 \)
5. \( N = 3, O = 1, G = 6, U = 7, H = 0, T = 5 \)

These combinations satisfy the equation. Would you like more details on how a specific solution works or any further clarification?

Here are five related questions to deepen your understanding:
1. What strategy is commonly used to solve cryptarithms?
2. Can cryptarithms have more than one solution?
3. How does trial and error play a role in solving cryptarithms?
4. What types of cryptarithms are more complex than this one?
5. How can logic puzzles like this improve problem-solving skills?

**Tip:** When solving cryptarithms, always start by narrowing down digits for the highest place values first, as they provide the most constraints.

Discover how to solve the cryptarithm NO + GUN + NO = HUNT using algebraic equations and number theory. This problem involves assigning unique digits to letters to satisfy the equation. Suitable for students in Grades 9-12.

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