The total number of 3 digit numbers which have two or more consecutive digits identical is

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Answer:- 1

Explanation:-

Solution:

In each set of 100 numbers, there are 10 numbers whose tens digit and unit digit are same. Again in the same set there are 10 numbers whose hundreds and tens digits are same. But one number in each set of 100 numbers whose Hundreds, Tens and Unit digit are same as 111, 222, 333, 444 etc Hence, there are exactly (10 + 10 - 1) = 19 numbers in each set of 100 numbers. Further there are 9 such sets of numbers Therefore such total numbers = 19 × 9 = 171 Alternatively,

9 × 10 × 10 - 9 × 9 × 9 = 900 - 729 = 171

The number of three digit numbers having only two consecutive digits identical is Considering the end digits to be identical, we get total 90 numbers out of which 9 are starting with zero.Hence total 3 digit numbers with the ending digits identical are 90-9=81.SimilarlyConsidering the starting digits to be identical, we get total 90 numbers out of which 9 are starting with zero.Hence total 3 digit numbers with the starting digits identical are 90-9=81.Hence the total number of 3 digit numbers with two consecutive identical digits are$$81+81$$$$=2(81)$$$$=162$$

The number of three digit numbers having only two consecutive digits identical is