The numbers 1 - 26 have been randomly assigned to the letters of the alphabet.
The numbers beside each word are the total of the values assigned to the letters in the word. e.g for LYRE L,Y,R,E might equal 5,9,20 and 13 respectively or any other combination that add up to 47.
The problem - What is the value of D ?
BALLET 45;
POLKA 59
CELLO 43;
QUARTET 50
CONCERT 74;
SAXOPHONE 134
FLUTE 30;
SCALE 51
FUGUE 50;
SOLO 37
GLEE 66;
SONG 61
JAZZ 58;
SOPRANO 82
LYRE 47;
THEME 72
OBOE 53;
VIOLIN 100
OPERA 65;
WALTZ 34
A problem from. 'Tough Puzzles'.
DefDbl A-Z
Dim crlf$, used(-100 To 100)
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr(13) + Chr(10)
For o = 1 To 26
If used(o) = 0 Then
used(o) = 1
For b = 1 To 26
If used(b) = 0 And 2 * o + b < 53 Then
used(b) = 1
e = 53 - (2 * o + b)
If e < 27 Then
If used(e) = 0 Then
used(e) = 1
For s = 1 To 26
If used(s) = 0 Then
used(s) = 1
l = 37 - s - 2 * o
If l > 0 And l < 27 And used(l) = 0 Then
used(l) = 1
For n = 1 To 26
If used(n) = 0 Then
used(n) = 1
g = 61 - s - o - n
If g > 0 And g < 27 And e = (66 - g - l) / 2 And used(g) = 0 Then
used(g) = 1
If e = Int(e) And e > 0 And e < 27 Then
c = 43 - e - o - 2 * l
If c > 0 And c < 27 And used(c) = 0 Then
used(c) = 1
a = 51 - s - c - l - e
If a > 0 And a < 27 And used(a) = 0 Then
used(a) = 1
rt = 74 - 2 * c - o - n - e
For r = 1 To 26
t = rt - r
If t > 0 And t < 27 And used(r) = 0 And used(t) = 0 Then
If b + a + 2 * l + e + t = 45 Then
used(r) = 1: used(t) = 1
qu = 50 - a - r - e - 2 * t
For q = 1 To 26
u = qu - q
If q > 0 And q < 27 And used(q) = 0 And used(u) = 0 Then
used(q) = 1: used(u) = 1
f = 50 - u - g - u - e
If f > 0 And f < 27 And used(f) = 0 Then
used(f) = 1
If f + l + u + t + e = 30 Then
Text1.Text = Text1.Text & " a b c d e f g h i j k l m n o p q r s t u v w x y z" & crlf
Text1.Text = Text1.Text & mform(a, "###") & mform(b, "###") & mform(c, "###") & " " & mform(e, "###") & mform(f, "###") & mform(g, "###") & " " & mform(l, "###") & " " & mform(n, "###") & mform(o, "###") & " " & mform(q, "###") & mform(r, "###") & mform(s, "###") & mform(t, "###") & mform(u, "###") & crlf
End If
used(f) = 0
End If
used(q) = 0: used(u) = 0
End If
Next
used(r) = 0: used(t) = 0
End If
End If
Next
used(a) = 0
End If
used(c) = 0
End If
DoEvents
End If
used(g) = 0
End If
used(n) = 0
End If
Next n
used(l) = 0
End If
used(s) = 0
End If
Next s
used(e) = 0
End If
End If
used(b) = 0
End If
Next
used(o) = 0
End If
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
was sufficient to find a unique solution and identifying some of the letters for that solution:
a b c d e f g h i j k l m n o p q r s t u v w x y z
5 13 9 20 4 24 2 12 10 7 11 15 3 1
manually I was able to expand this to
a b c d e f g h i j k l m n o p q r s t u v w x y z
5 13 9 20 4 24 23 2 12 10 19 7 11 15 3 1 17
Also found manually were:
J + 2*Z = 53
H + M = 28
V + 2*I = 76
W + Z = 24
Due to constraints imposed by previously unassigned letters, H and M must be 6 and 22 in order to add to 28; W and Z must be 8 and 16 to add to 24; V must be 26 and I must be 25. Finally Z must be the 16 of the 8 and 16 pair,so J is identified as being 21 by the first of these last four equations.
That leaves D = 14.
Edited on May 27, 2018, 3:10 pm
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Posted by Charlie
on 2018-05-27 15:08:52 |
computer to narrow the problem, then analysis of what's left
