This puzzle follows a non-standard pattern, so let's look for relationships between the numbers in each equation:

• $4 + 6 = 4$
• $3 + 6 = 1$
• $5 + 3 = 3$
• $8 + 2 = 9$

One possible observation is that the right side is not the result of traditional addition. The pattern seems to involve taking the difference between the numbers involved:

1. $4 + 6 \rightarrow |4 - 6| = 2$, but the answer given is 4.
2. $3 + 6 \rightarrow |3 - 6| = 3$, but the answer given is 1.
3. $5 + 3 \rightarrow |5 - 3| = 2$, but the answer given is 3.
4. $8 + 2 \rightarrow |8 - 2| = 6$, but the answer given is 9.

The pattern of results doesn't follow a strict numerical rule like subtraction or addition, so it seems more like an arbitrary or specific rule for the puzzle, possibly based on a visual or positional code rather than pure arithmetic.

For $7 + 1$, following this puzzle's unpredictable pattern, the answer might similarly break away from traditional logic. Since the given answers don’t directly follow mathematical rules, a plausible guess for $7 + 1$ could be 8, maintaining the use of near-random answers based on the previous equations.

Would you like more details on this puzzle?

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Here are five related questions:

1. How can puzzles like these help improve critical thinking in math?
2. What other types of puzzles rely on non-traditional math patterns?
3. Can puzzles with illogical patterns be solved using systematic reasoning?
4. How might positional number puzzles differ from traditional math problems?
5. Are there ways to create similar puzzles using visual or geometric patterns?

Tip: Always check if a puzzle uses a mathematical trick, a pattern, or a logic twist.