Question 662241
<pre>
Let the integer = N

Next integer = N+1

Previous integer = N-1

Half the next integer = {{{(N+1)/2}}}

One third the previous integer = {{{(N-1)/3}}} 

{{{(matrix(5,1,

Half,of,the,next,integer))}}} &#8807; {{{(matrix(6,1,

One,third,of,the,previous,integer))}}} + 4

    {{{(N+1)/2}}} &#8807;  {{{(N-1)/3}}} + 4 

  3(N+1) &#8807; 2(N-1) + 24

    3N+3 &#8807; 2N-2 + 24

       N &#8807; 19
    
19 is the least possible value of N

Edwin</pre>