The number 1.5 is special because it is equal to one quarter of the sum of its digits, as 1+5=6 and 64=1.5 .Find all the numbers that are equal to one quarter of the sum of their own digits.

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Aliana Porter · Accepted Answer

Step 1This is not much better than a brute force method:The sum of the digits S is a non-negative integer, so a quarter of it&amp;nbsp;S4&amp;nbsp;s non-negative, of the form x or x.25 or x.5 or x.75 for some non-negative integer x.We must have&amp;nbsp;x&amp;lt;10&amp;nbsp;since if&amp;nbsp;10≤x&amp;lt;100&amp;nbsp;then&amp;nbsp;40≤4x≤S&amp;lt;412&amp;nbsp;so the sum of the digits of x must be at least&amp;nbsp;40−12=28&amp;nbsp;but two-digit integers have sums of digits no more than 18. Similarly with larger x.So a satisfactory x has sum of digits&amp;nbsp;4x=S=x&amp;nbsp;with solution&amp;nbsp;x=0and a satisfactory&amp;nbsp;x.&amp;nbsp;25&amp;nbsp;has sum of digits4(x+14)=S=x+7with solution&amp;nbsp;x=2and a satisfactory&amp;nbsp;x.&amp;nbsp;5&amp;nbsp;has sum of digits4(x+12)=S=x+5with solution&amp;nbsp;x=1and a satisfactory&amp;nbsp;x.&amp;nbsp;75&amp;nbsp;has sum of digits4(x+34)=S=x+12with solution&amp;nbsp;x=3making the numbers which work0,&amp;nbsp;2.25,&amp;nbsp;1.5,&amp;nbsp;3.75

The number 1.5 is special because it is equal to

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