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

Question

Infinity Learn · Accepted Answer

Using $$2$$, $$5$$ and $$7$$ with repetition each place of n digit number can be chosen in $$3$$ ways. Hence, total number of $$n-$$ digit numbers $$=$$ $$3$$ × $$3$$ ×$$3$$ … n times $$=$$ $$3n$$.According to given condition $$3n$$ ≥ $$900$$ ⇒ $$3n$$–$$2$$ ≥ $$100$$.∴ n – $$2$$ ≥ $$5$$ ⇒ n ≥ $$7$$.

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

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