Question 1179051
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The three numbers are either 1- or 2-digit numbers, because their sum is 100.<br>
There can't be two numbers in the 60s, because the sum would be more than 100.<br>
Since each number must have at least one 6, there is one number in the 60s.<br>
The other two numbers have to have units digit 6, because their tens digits are not 6.<br>
To make a sum of 100, the units digit of the number in the 60s must be 8.<br>
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.<br>
ANSWER: The largest number is 68.<br>
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.<br>