An n-digit number is a positive number with exactly n digits. Nine hundered distinct n-digit numbers are to be formed using only three digits 2, 5 and 7.The smallest value of n for which this is possible is ___

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Solution

Distinct n digit numbers which can be formed using digits 2, 5 and 8 are $3^{n} .$
We have to find n so that $3^{n} \geq 900 \Rightarrow 3^{n - 2} \geq 100 \Rightarrow n - 2 \geq 5 \Rightarrow n \geq 7$
So the least value of n is 7 .

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An n-digit number is a positive number with exactly n digits. Nine hundered distinct n-digit numbers are to be formed using only three digits 2, 5 and 7.The smallest value of n for which this is possible is ___

Distinct n digit numbers which can be formed using digits 2, 5 and 8 are 3n. We have to find n so that 3n≥900⇒3n−2≥100⇒n−2≥5⇒n≥7 So the least value of n is 7 .

Distinct n digit numbers which can be formed using digits 2, 5 and 8 are $3^{n} .$
We have to find n so that $3^{n} \geq 900 \Rightarrow 3^{n - 2} \geq 100 \Rightarrow n - 2 \geq 5 \Rightarrow n \geq 7$
So the least value of n is 7 .