Discussion

Explanation:

Single-digit such numbers = 9

2-digit such numbers: __ __
Ten’s digit can be filled in 9 ways (i.e., 1, 2, 3, …, 9)
Unit’s digit can be filled in 9 ways (i.e., any of the 10 single digits except the one at ten’s place)
⇒ Total such 2-digit numbers = 9 × 9 = 81

3-digit such numbers: __ __ __
Hundred’s digit can be filled in 9 ways (i.e., 1, 2, 3, …, 9)
Ten’s digit can be filled in 9 ways (i.e., any of the 10 single digits except the one at hundred’s place)
Unit’s digit can be filled in 8 ways (i.e., any of the 10 single digits except the ones at hundred’s and ten’s place)
⇒ Total such 3-digit numbers = 9 × 9 × 8 = 648

∴ Total such numbers = 9 + 81 + 648 = 738.

Hence, option (c).

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