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 Clever counting (Posted on 2015-08-07)
Some positive integers n have the property that the sum
[ n + reverse(n) ] consists entirely of odd (decimal) digits.
For instance, 36 + 63 = 99 and 409 + 904 = 1313.
We will call such numbers reversible; so 36, 63, 409, and 904 are reversible. Leading zeroes are not allowed in either n or reverse(n).
There are 120 reversible numbers below one-thousand.

a. Evaluate how many reversible numbers are there
below 10k, k=2,3... up to 6 or 7 .

b. Analyze the results, aiming to find the relation (i.e. approximate function) between N(k) and k.

Source: Project Euler, modified.

 No Solution Yet Submitted by Ady TZIDON No Rating

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 part a computer solution | Comment 1 of 6
Limit is followed by number under that limit:

100 20
1000 120
10000 720
100000 720
1000000 18720
10000000 68720

DefDbl A-Z
Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

rept = 100
For n = 1 To 10000000
If n Mod 10 > 0 Then
ns\$ = LTrim(Str(n))
nrs\$ = ""
For i = 1 To Len(ns)
nrs = Mid(ns, i, 1) + nrs
Next
tot\$ = LTrim(Str(n + Val(nrs)))
good = 1
For i = 1 To Len(tot)
If InStr("13579", Mid(tot, i, 1)) = 0 Then good = 0: Exit For
Next
If good Then ct = ct + 1
End If
If n = rept Then
Text1.Text = Text1.Text & rept & Str(ct) & crlf
rept = 10 * rept
DoEvents
End If
Next

Text1.Text = Text1.Text & ct & crlf & " done"

End Sub

 Posted by Charlie on 2015-08-07 18:59:07

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