Question

Make the greatest and the smallest \[4\] -digit number using any four different digits with the given conditions.
A. \[4\] is always in the thousands place
B. \[0\] is always in the hundreds place
C. \[6\] is always in one's place.

Answer 1

Hint: To solve this question you need to analyse the question to begin with. Now in each condition it tells us to find a \[4\] digit number with different numbers with different numbers in certain places. Now we find answers to all these logics using the logic of highest and lowest numbers.

Complete step-by-step answer:
For the first condition \[4\] is always in the thousands place now since it is a four digit number therefore there will be digits at tens hundreds and thousands place. \[4\] being in the thousands place for the first part of the question. All the different digits that can be used by you to make different numbers are \[0,1,2,3,4,5,6,7,8,9\] .
Since we already know that \[4\] is already in the thousands place therefore the numbers now left for the other positions are
 \[0,1,2,3,5,6,7,8,9\] .
For the greatest four digit number, the number at hundred places should be the greatest of all the other numbers left. So digit \[9\] will be at hundreds places. No digits can be repeated therefore the numbers left are \[0,1,2,3,5,6,7,8\] . The number at tens should in the same way be the biggest of these digits. Therefore digit \[8\] will be placed at tens place and likewise out of \[0,1,2,3,5,6,7\] the number at one's digit will be \[7\] . Hence the greatest number will be \[4987\] . Likewise for the smallest number the number at hundreds place will be \[1\] ,tens place be \[2\] and ones be \[3\] . The smallest number being. \[4123\] .
Now using this same method for condition two we get the answer that if \[0\] is at hundreds place the biggest number will be \[9087\] and smallest will be \[1023\] .
Now using this same method for condition two we get the answer that if \[6\] is at one place the biggest number will be \[9876\] and smallest will be \[1026\] .

Note: : \[0\] can never be at thousands places or the number will be a three digit number and not a four digit number. The number “0” holds its value only when its added after certain digits not before.