We need to interpret the given mathematical expression $13 \div 5 \times 6 - 2 + 12$ based on the provided substitution rules:

1. $+$ means $\div$
2. $\times$ means $-$
3. $\div$ means $+$
4. $-$ means $\times$

Substituting these rules into the expression:

Original Expression:

$13 \div 5 \times 6 - 2 + 12$

After Substitution:

$13 + 5 - 6 \times 2 \div 12$

Following Order of Operations (BODMAS):

1. Handle $\times$ and $\div$ first:
   • $6 \times 2 = 12$
   • $12 \div 12 = 1$

Now the expression becomes: $13 + 5 - 1$

2. Handle $+$ and $-$ next:
   • $13 + 5 = 18$
   • $18 - 1 = 17$

Final Answer:

$\boxed{17}$

Would you like detailed explanations for substitutions, or do you have further questions?

Related Questions:

1. How does BODMAS/PEDMAS affect the order of operations here?
2. What if the substitution rules were reversed? How would it change the solution?
3. Can this approach be applied to more complex expressions with more operators?
4. How does symbolic substitution help in solving logical puzzles?
5. What are other types of similar substitution puzzles?

Tip:

Always rewrite the entire expression after applying substitutions to avoid confusion with the original operators.