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  • Sum of all three digit numbers (no digit being zero) having the property that all digits are perfect squares, isOption: 1 3108<div clas

Sum of all three digit numbers (no digit being zero) having the property that all digits are perfect squares, is

Option: 1

3108


Option: 2

6216


Option: 3

13986


Option: 4

none of these


Answers (1)

best_answer

The non-zero perfect square digits are 1, 4 and 9.

1 can occur at units place in  3 \times 3=9 ways.

\therefore  Sum due to 1 at units place is 1 \times 9. Similarlys. due to 1 at tens place is 1 \times 1 \times 9. Similarly, sum at hundreds place is 1 \times 10 \times 9 and sum due to 1 the digits 4 and 9 is 1 \times 100 \times 9. We can deal with Thus, sum of the desired number is

(1+4+9)(1+10+100)(9)=13986

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chirag

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