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Analyzing change (Posted on 2014-10-28) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution 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

Private Sub Form_Load()
 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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