Question

Form the greatest and smallest five-digit numbers by using following digits with only one digit twice:

$1, 6, 2, 8$

Accepted Answer

Steps for the formation of the greatest number where digits can be repeated:

Step (i): Do not place zero at the leftmost place.

Step (ii): For the largest (i.e. greatest) number, start placing the digits from the leftmost place and proceed towards the right.

Step (iii): Fill up the places with the digits in descending order. Use the biggest digit the maximum number of times or as stated in the problem.

Thus, we shall use the biggest digit $8$ twice in the beginning, followed by the digits $6, 2$ and $1$ .

So, the greatest number is $88621$ .

Steps for the formation of the smallest number where digits can be repeated:

Step (i): Do not place zero at the leftmost place.

Step (ii): For the smallest number, start placing the smallest non-zero digit from the leftmost place and proceed towards the right.

Step (iii): Fill up the places with the digits in ascending order. Use the smallest digit the maximum number of times or as stated in the problem.

Thus, we shall use the smallest non-zero digit $1$ twice in the beginning, followed by the digits $2, 6$ and $8$ .

So, the smallest number is $11268$ .

Therefore, the required greatest and smallest five-digit numbers are $88621$ and $11268$ , respectively.

CHAPTER-END EXERCISES

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