Question 1179051
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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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<pre>
The greatest number is 68.      <U>ANSWER</U>


Two other numbers are 16 and 16.


<U>CHECK</U>.  68 + 16 + 16 = 100.
</pre>


Solved.  &nbsp;&nbsp;&nbsp;&nbsp;Easy mental exercise.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>Explanation</U>


<pre>
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.
</pre>

Solved.


Easy mental exercise.