A three-digit number n is such that the last two digits of it are equal and differ from the first. The number of such n's is

1) 64

2) 72

3) 81

4) 900

Answer: (3) 81

Solution: The hundreds place of three digit numbers can be filled with digits 1 to 9, since 0 is excluded.

Now, the digit at tens place can be filled in 9 ways, excluding the digit that is included in hundreds place.

Now the unit place can be filled in only 1 way, since the last two digits are equal and differ from the first digit.

Therefore, total number of ways = 9 x 9 x 1 = 81

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