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 Celsius Fahrenheit Check (Posted on 2015-01-13)
S(x) denotes the sum of squares of the digits. For example:
S(97) = 92 + 72 = 130.

Find all possible positive integer values of N < 2014 such that:
N oF= (S(N) - 5) oC

N.B.: F = (9/5)*C + 32

*** As an extra challenge, solve this puzzle using a non computer program assisted method.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 not taking up the extra challenge--(spoiler) Comment 1 of 1
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For n = 1 To 2014
rhs = (sosqd(n) - 5) * 9 / 5 + 32
If rhs = n Then
Text1.Text = Text1.Text & n & Str(sosqd(n)) & Str(rhs) & crlf
End If
Next

Text1.Text = Text1.Text & "done"

End Sub

Function sosqd(n)
s\$ = LTrim(Str(n))
tot = 0
For i = 1 To Len(s\$)
tot = tot + Val(Mid(s\$, i, 1)) * Val(Mid(s\$, i, 1))
Next
sosqd = tot
End Function

finds

185 90 185

N is 185, which is 85°C, having subtracted 5 from the sum of the squares of the digits, which is 90.

That's the only solution.

 Posted by Charlie on 2015-01-13 14:38:01

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