Question

write the greatest 5 digit number greater than 86542 with no digit repeated​

Answer 1

Answer:

57310

Step-by-step explanation:

Well, let’s think this out: the number cannot start with 9, because then there’s no way the second digit could be greater than the first. It cannot start with 8, because there is only one digit greater than 8, but 4 digits left in the number. If you follow my logic, you’ll figure out that the greatest digit you can place in the first position is 5. There are four digits greater than five, and four slots left to place them in.

Answer 2

Assuming base ten, the largest digit is 9, and goes in the highest position, and then the next largest, the next largest, the next largest and finally the next largest:

98765

If you are using the absolute value to determine “great” (that is to say, if -2>1, because -2 is further from 0) then -98765 is just as great.

In base n the answer is the digits n-1, n-2, n-3, n-4, n-5 in that order

In base four and lower, no such number exists, as there aren’t five digits in the base, you must repeat at least one to have a five digit number

In base five, the number is 43210

In octal, the number is 76543

In hexadecimal the number is fedcb

and so forth.

Since bases continue to infinity, for any base n with a five digit number as described in the formula, there will always be a base n+1 with a greater largest five digit number.

And again, if you’re using the absolute value definition, then the negative of each of those numbers is equally great, meaning that there’s never a “greatest” number.