Question

In a new decimal system, digits 0–9 are replaced with symbols. Equations are given. In (iv), one digit appears twice. Which digit replaces the question mark? 

Hint:

When solving symbolic arithmetic, first confirm that the operations (+, −) are standard. Then replace symbols step by step with real digits.

Answer 1

Step 1: Decode the given examples.
Equation (i): Symbol $1 + 4 = 5$.
Equation (ii): Symbol $2 + 2 = 4$.
Equation (iii): Symbol $10 - 4 = 6$.
So, the rules of arithmetic are unchanged. Only symbols are different.
Step 2: Equation (iv).
It reads as four copies of one digit + four copies of another digit.
So the form is:
\[ 1111 + 4444 \] Step 3: Perform addition. \[ 1111 + 4444 = 5555 \] Step 4: Check condition.
The problem says "one digit appears twice in the solution."
Here, digit 5 repeats four times, so the repeating digit is 5.
Final Answer: \[ \boxed{5} \]