The number of numbers from 1 to 1 0 6 (both inclusive) in which two consecutive digits are same is equal to 402128 + K where K is a single digit number then K must be equal to ____ .

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TestHub · Accepted Answer

No.of n digit numbers in which no two consecutive digits are same $= 9^{n}$

⇒ no.of numbers from 1 to $1 0^{6}$ in which no two consecutive digits are same $= \sum_{n = 1}^{6} 9^{n} = 597870$

Required number $= 1 0^{6} - 597870 = 402130 = 402128 + 2$

$K = 2$

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