Form the greatest and smallest $7$ -digit numbers using the digits $1, 4, 9, 2, 5, 6 a n d 3$ only once.

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Solution

Step 1: Write the greatest $7$ -digit number using the given digits
To find the greatest number formed by using any digits, we arrange them in descending order.
Therefore, the greatest 7-digit number formed using the digits $1, 4, 9, 2, 5, 6 a n d 3$ $= 96, 54, 321$
Step 2: Write the smallest $7$ -digit number using the given digits.
To find the greatest number formed by using any digits, we arrange them in ascending order.
Therefore, the smallest 7-digit number formed using the digits $1, 4, 9, 2, 5, 6 a n d 3$ $= 12, 34, 569$ .
Hence, the required greatest and smallest numbers are $96, 54, 321$ and $12, 34, 569$ respectively.

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