In this coding puzzle, a custom set of operations is defined: A*B means A multiplied by B, A@B means A divided by B, A?B means B added to A and A=B means B subtracted from A. Using these rules and normal precedence, what is the value of 10*10 = 5*10 ? 50@10 ?

Introduction / Context:
This question introduces four non standard operator symbols *, @, ? and =, each with a specific arithmetic meaning. The expression 10*10 = 5*10 ? 50@10 must be evaluated using these coded meanings, not the usual ones. The problem checks whether you can translate the entire expression carefully and then apply normal precedence of multiplication and division before performing addition and subtraction.

Given Data / Assumptions:

• A*B means A multiplied by B, so A*B = A * B.
• A@B means A divided by B, so A@B = A / B.
• A?B means add B to A, so A?B = A + B.
• A=B means subtract B from A, so A=B = A - B.
• Expression: 10*10 = 5*10 ? 50@10.
• Normal precedence applies after decoding: multiplication and division first, then addition and subtraction from left to right.

Concept / Approach:
The method is to replace each occurrence of *, @, ? and = with their true operations. Once this is done, the expression becomes an ordinary arithmetic expression with standard operators. You then carry out multiplication and division first, followed by addition and subtraction. Care must be taken to interpret = as subtraction and not as equality, as its meaning has been overloaded here in a special way.

Step-by-Step Solution:
Step 1: Start from the coded expression: 10*10 = 5*10 ? 50@10. Step 2: Decode each operator using the given meanings. 10*10 means 10 * 10. Between 10 and 5, the symbol = means subtract B from A, so 10 = 5 means 10 - 5. 5*10 means 5 * 10. ? represents addition, so ? 50 means + 50. @ represents division, so 50@10 means 50 / 10. Step 3: Combine these pieces into one standard expression. 10 * 10 - 5 * 10 + 50 / 10. Step 4: Evaluate all multiplication and division first. 10 * 10 = 100. 5 * 10 = 50. 50 / 10 = 5. Step 5: Substitute back: 100 - 50 + 5. Step 6: Evaluate subtraction and addition from left to right. 100 - 50 = 50. 50 + 5 = 55.

Verification / Alternative check:
A quick check is to recompute each of the three basic operations to confirm no multiplication or division error has occurred. Since 10 * 10 = 100, 5 * 10 = 50 and 50 / 10 = 5 are all straightforward, combining them as 100 - 50 + 5 gives 55 without ambiguity. Any alternative interpretation of = as equality or ? as something other than addition would conflict with the definitions given in the question. Because the decoded expression is unique and evaluates to 55, this answer is secure.

Why Other Options Are Wrong:
Options 100, 45 and 65 often come from errors such as adding instead of subtracting at the = position, or failing to perform the division by 10. Option 1000 misinterprets the expression as 10 * 10 * 5 * 10 with no subtraction or division at all. These values do not follow from the explicit definitions of the coded operators and so cannot be valid. Only 55 is consistent with both the decoding and correct arithmetic evaluation.

Common Pitfalls:
A major pitfall is to treat = as an equality sign and try to form an equation to be solved, which is not what the question intends. Another is to work directly on the coded expression without writing the decoded version, which can lead to mixing up the meanings of @ and ?, especially under time pressure. Always rewrite the expression clearly in terms of normal operators and then apply precedence rules methodically.

Final Answer:
Under the given definitions of *, @, ? and =, the value of 10*10 = 5*10 ? 50@10 is 55.