My number consists of 3 digits in strictly increasing order. It is a semiprime number, both factors terminating by the same digit.
Find it.
Bonus: is there a solution for 4-digit number?
I didn't include perfect squares, but I still had 10 solutions for the 3-digit case as did xdog: I have 489 and 579 instead of his two squares. The numbers are followed by their two factors each.
129 3 43
159 3 53
249 3 83
259 7 37
469 7 67
489 3 163
579 3 193
679 7 97
689 13 53
789 3 263
Perhaps 689 best fills the spirit of the question as each factor has more than one digit, so they can terminate in the same digit, rather than one being the terminating digit of the other.
In the 4-digit case:
1379 7 197
1389 3 463
1469 13 113
1569 3 523
1589 7 227
1679 23 73
1689 3 563
2359 7 337
2369 23 103
2469 3 823
2479 37 67
2569 7 367
2589 3 863
3459 3 1153
3489 3 1163
3569 43 83
3579 3 1193
3589 37 97
3679 13 283
4569 3 1523
4589 13 353
5789 7 827
Again this does not include any perfect squares that may satisfy the condition trivially (as far as matching terminal digits).
DefDbl A-Z
Dim crlf$, fct(20, 1)
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
For n = 111 To 10000
f = factor(n)
If f = 2 Then
If fct(1, 1) = 1 And fct(2, 1) = 1 Then
If fct(1, 0) Mod 10 = fct(2, 0) Mod 10 Then
ns$ = LTrim(Str(n))
good = 1
For i = 1 To Len(ns) - 1
If Mid(ns, i + 1, 1) <= Mid(ns, i, 1) Then good = 0: Exit For
Next
If good Then Text1.Text = Text1.Text & n & Str(fct(1, 0)) & Str(fct(2, 0)) & crlf
End If
End If
End If
DoEvents
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
Function factor(num)
diffCt = 0: good = 1
n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
dv = 2: GoSub DivideIt
dv = 3: GoSub DivideIt
dv = 5: GoSub DivideIt
dv = 7
Do Until dv > limit
GoSub DivideIt: dv = dv + 4 '11
GoSub DivideIt: dv = dv + 2 '13
GoSub DivideIt: dv = dv + 4 '17
GoSub DivideIt: dv = dv + 2 '19
GoSub DivideIt: dv = dv + 4 '23
GoSub DivideIt: dv = dv + 6 '29
GoSub DivideIt: dv = dv + 2 '31
GoSub DivideIt: dv = dv + 6 '37
If INKEY$ = Chr$(27) Then s$ = Chr$(27): Exit Function
Loop
If n > 1 Then diffCt = diffCt + 1: fct(diffCt, 0) = n: fct(diffCt, 1) = 1
factor = diffCt
Exit Function
DivideIt:
cnt = 0
Do
q = Int(n / dv)
If q * dv = n And n > 0 Then
n = q: cnt = cnt + 1: If n > 0 Then limit = Sqr(n) Else limit = 0
If limit <> Int(limit) Then limit = Int(limit + 1)
Else
Exit Do
End If
Loop
If cnt > 0 Then
diffCt = diffCt + 1
fct(diffCt, 0) = dv
fct(diffCt, 1) = cnt
End If
Return
End Function
|
|
Posted by Charlie
on 2019-01-05 13:47:53 |
computer solutions
