Step 1: Identify the possible digits
The digits must be perfect squares and cannot be zero. The available digits from {1,2,…,9} that are perfect squares are:
Step 2: Determine the total number of such 3-digit numbers
Since each of the three positions (hundreds, tens, and units) can be filled by any of the 3 available digits:
Step 3: Find the sum of digits at each position
In these 27 numbers, each digit (1,4,9) will appear an equal number of times in the hundreds, tens, and units place.
Occurrences per digit at each place=327=9 times
Sum of digits at any single position (units, tens, or hundreds):
Sum of one position=9×(1+4+9)
Sum of one position=9×14=126
Step 4: Calculate the total sum
The total sum is the sum of the values of the digits at their respective places:
Total Sum=(100×126)+(10×126)+(1×126)
The sum of all such three-digit numbers is 13986.
Correct Option: (c)
