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Solution :

3 digit number:(100x+10y+z)<br>
`x^2+y^2+z^2=19`<br>
`x-1,y-1,z-1`<br>
(n,1),n,(n+1)<br>
`(n-1)^2+n^2+(n+1)^2=149`<br>
`n^2-2n+1+n^2+n^2+2n+1=149`<br>
`3n^2+2=149`<br>
`3n^2=147`<br>
`n^2=49`<br>
n=7<br>
n-1=6<br>
n+1=8<br>
Min(6,7,8)=6.
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