The sum of all three-digit numbers,formed usi | vedclass

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Question

(A) The non-zero digits that are perfect squares of a natural number are $1, 4,$ and $9$.Since we need to form three-digit numbers using these $3$ dig

Vedclass · Accepted Answer

$13986$

Vedclass · Answer

(A) The non-zero digits that are perfect squares of a natural number are $1, 4,$ and $9$.Since we need to form three-digit numbers using these $3$ digits,the total number of such digits available is $n = 3$.The number of possible three-digit numbers is $3^3 = 27$.In each position (hundreds,tens,and units),each digit $(1, 4, 9)$ appears $3^2 = 9$ times.The sum of the digits is $1 + 4 + 9 = 14$.The sum of the numbers is given by: $(1 + 4 + 9) 	imes 9 	imes (100 + 10 + 1) = 14 	imes 9 	imes 111 = 126 	imes 111 = 13986$.

The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is:

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