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 Analyzing change (Posted on 2014-10-28)
In Dingistan the coins are of the following denomination:
SILVER: 10, 15, and 20 dingos
COPPER: 1, 2, and 3 dingos.
The ACMs (automatic change machines) accept silver coins and return change as follows:
20d=(15+2+2+1) d
15d=(10+2+2+1) d
10d=(3+3+2+2) d

After Dingus converted into copper the 145d he had in silver coins, his friend W.G.Ringus counted them and successfully reconstructed the original composition of silver coins, previously unknown to him.

It is up to you to find both the input and the output
- if the Wise Guy did it – you can do it, too.

It is D4, if solved analytically.

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 3 of 4 |
DefDbl A-Z
Dim crlf\$
Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

totAmt = 145
For n20 = 0 To totAmt / 20
rem1 = totAmt - n20 * 20
For n15 = 0 To rem1 / 15
rem2 = rem1 - n15 * 15
If rem2 Mod 10 = 0 Then
n10 = rem2 / 10
sub20 = n20: sub15 = n15: sub10 = n10
n1 = sub20: n2 = 2 * sub20: n3 = 0
sub15 = sub15 + sub20
n1 = n1 + sub15: n2 = n2 + 2 * sub15
sub10 = sub10 + sub15
n2 = n2 + 2 * sub10: n3 = n3 + 2 * sub10
Text1.Text = Text1.Text & mform(n1, "###0") & mform(n2, "###0") & mform(n3, "###0")
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & mform(n20, "###0") & mform(n15, "###0") & mform(n10, "###0")
Text1.Text = Text1.Text & crlf
End If
Next n15
Next n20

Text1.Text = Text1.Text & crlf & "done"
End Sub

produces an output that after sorting and annotating is:

`   observed          original  1d  2d  3d      20d  15d 10d   1  30  28        0   1  13   3  32  26        0   3  10   3  32  26        1   1  11   5  34  24        0   5   7   5  34  24        1   3   8   5  34  24        2   1   9   7  36  22        0   7   4   7  36  22        1   5   5   7  36  22        2   3   6   7  36  22        3   1   7   9  38  20        0   9   1   9  38  20        1   7   2   9  38  20        2   5   3   9  38  20        3   3   4   9  38  20        4   1   5  11  40  18        2   7   0  11  40  18        3   5   1  11  40  18        4   3   2  11  40  18        5   1   3  13  42  16        5   3   0  13  42  16        6   1   1`

Only the top row is unique for observed values: Dingus originally had 13 10d pieces and 1 15d piece, which were converted to 28 3d pieces, 30 2d pieces and 1 1d piece.

 Posted by Charlie on 2014-10-28 12:22:14

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