SOLUTION: The sum of three distinct whole numbers is 100. Each of the three numbers contains at least one digit 6. What is the greatest of the three numbers?

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Question 1179051: The sum of three distinct whole numbers is 100. Each of the three numbers contains at least one digit 6. What is the greatest of the three numbers?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52812)   (Show Source): You can put this solution on YOUR website!
.
The sum of three distinct whole numbers is 100.
Each of the three numbers contains at least one digit 6.
What is the greatest of the three numbers?
~~~~~~~~~~~~~ 


The greatest number is 68.      ANSWER


Two other numbers are 16 and 16.


CHECK.  68 + 16 + 16 = 100.


Solved.     Easy mental exercise.


                        Explanation 

In order for the greater number would be greatest possible, two other numbers should be smallest possible.


So, we consider several smaller number pairs  (6,6),  (6,16),  (16,6)  and (16,16).


The pair  (6,6)  has the sum 12, leaving  100-12 = 88 for the greater number, which does not work.


The pair  (6,16)  has the sum 22, leaving  100-22 = 78 for the greater number, which does not work.


The pair  (16,6) is the same as (6,16), i.e. does not work.


Finally, the pair (16,16) has the sum 32, leaving  100-32 = 68 for the greater number,  which  DOES WORK,  fortunately.

Solved.

Easy mental exercise.




Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


The three numbers are either 1- or 2-digit numbers, because their sum is 100.

There can't be two numbers in the 60s, because the sum would be more than 100.

Since each number must have at least one 6, there is one number in the 60s.

The other two numbers have to have units digit 6, because their tens digits are not 6.

To make a sum of 100, the units digit of the number in the 60s must be 8.

So one of the numbers is 68. Then the other two have a sum of 100-68=32; they both have units digit 6, and they are different numbers. There is only one possibility -- the other two numbers are 6 and 26.

ANSWER: The largest number is 68.

Note since the problem asked only for the largest of the three numbers, we did not need to find the two smaller numbers. But doing so makes the problem a bit more interesting.
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