A three-digit number in which the digit in the units place is the smallest of the three digits is such that the sum of the squares of the digits is 149.If each of the digit is replaced by its predecessor,the new number formed has two digits common with the original number.The digit in the units place of the original number is :

Explanation

3 digit number:(100x+10y+z)

`x^2+y^2+z^2=19`

`x-1,y-1,z-1`

(n,1),n,(n+1)

`(n-1)^2+n^2+(n+1)^2=149`

`n^2-2n+1+n^2+n^2+2n+1=149`

`3n^2+2=149`

`3n^2=147`

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