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

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(A) The non-zero digits that are perfect squares are $1, 4,$ and $9$.There are $3$ such digits.The total number of three-digit numbers that can be for

Vedclass · Accepted Answer

$13986$

Vedclass · Answer

(A) The non-zero digits that are perfect squares are $1, 4,$ and $9$.There are $3$ such digits.The total number of three-digit numbers that can be formed using these digits (with repetition allowed,as implied by the context of such problems) is $3 	imes 3 	imes 3 = 27$.Each digit $1, 4,$ and $9$ appears in the units,tens,and hundreds place exactly $9$ times each.The sum of the digits in any place is $9 	imes (1 + 4 + 9) = 9 	imes 14 = 126$.The sum of all such numbers is $126 	imes 100 + 126 	imes 10 + 126 	imes 1 = 126 	imes 111 = 13986$.

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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