Question 1144968
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The largest possible value, under the given conditions, is  27.


It is achieved for THIS set of integer positive numbers {1, 2, 27}.


<U>ANSWER</U>.   The largest possible value that any of those numbers can have is 27.




To get the answer, it is clear, that the two other numbers must be as small as it is possible, under the condition.


Thinking in this way,  you immediately obtain the equation


     {{{(1 + 2 + x)/3}}} = 10


from which you immediately obtain the solution  x = 27.
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