Question

five note cards each contain a different single-digit numbers.The cards are arranged to find the largest possible 5-digit number,then rearanged to find the smallest possible 5 digit number. the sum of these two numbers is 99089. what is the SUM of the 5 digits on the cards?

Answer 1

Solution: The largest number is 86521, the smallest number is 12568  and the sum of digits is 22.

Explanation:

Let the digits on cards be a, b, c, d and e. where $a>b>c>d>e>0$ because if the smallest digit is 0, then we get a four digit number on rearrangement.

To get the five digit greatest number we have to arrange these digits in descending order. So the greatest number is abcde.

To get the five digit greatest number we have to arrange these digits in descending order. So the smallest number is edcba.

It is given that the sum of greatest and smallest number is 99089.

When we add greatest and smallest number we noticed that the sum of c and c is 2c which is equal to 0. It is possible if c=0 or c=5. since c>0, therefore the value of c=5.

So the from the addition of unit digits we get e+a=9, there are many possibilities to get the sum 9 like 1+8, 2+7 and 3+6 because a>5 and e<5 since we have to find the greatest and smallest number so by hidden trial the value of e=1 and a=8. Similarly d+b=8, b>5 and d<5 by hidden trial the value of b=2 and d=6.

The digits are 8, 6, 5, 2 and 1, therefore  largest number is 86521, the smallest number is 12568  and the sum of digits is 22.