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Cash and chit (Posted on 2014-12-15) Difficulty: 3 of 5
In this puzzle there is a one-to-one correspondence between
10 distinct letters and the digits 0 to 9.
In the set of equations below both str1 and str2
are strings of 4 digits:

Given:
sqrt(str1 str2) = chit
and
sqrt(str2 str1) = cash

If 10265102493 is a valid English word, how much
( complying with the puzzle's coding) is q*z ?

Rem: sqrt(str1 str2) is a square root of an 8 digit number represented by a concatenation of the strings in the brackets.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solution Comment 1 of 1
 For c = 1 To 9
  used(c) = 1
 For h = 0 To 9
  If used(h) = 0 Then
    used(h) = 1
 For a = 0 To 9
  If used(a) = 0 Then
    used(a) = 1
 For t = 0 To 9
  If used(t) = 0 Then
    used(t) = 1
 For i = 0 To 9
  If used(i) = 0 Then
    used(i) = 1
    chit = 1000 * c + 100 * h + 10 * i + t
    sq1 = chit * chit
If sq1 > 9999999 And sq1 < 100000000 Then
 For s = 0 To 9
  If used(s) = 0 Then
    used(s) = 1
    cash = 1000 * c + 100 * a + 10 * s + h
    sq2 = cash * cash
    If sq2 > 9999999 And sq2 < 100000000 Then
      st1$ = LTrim(Str(sq1))
      st2$ = LTrim(Str(sq2))
      If Left(st1$, 4) = Right(st2$, 4) And Left(st2$, 4) = Right(st1$, 4) Then
        Text1.Text = Text1.Text & st1$ & "   " & st2$ & crlf
        Text1.Text = Text1.Text & cash & Str(chit) & crlf
        DoEvents
      End If
    End If
    used(s) = 0
  End If
 Next
End If
    used(i) = 0
  End If
 Next
    
    used(t) = 0
  End If
 Next
    used(a) = 0
  End If
 Next
    used(h) = 0
  End If
 Next
  used(c) = 0
 Next

finds

92968164   81649296  (squares)
9036 9642          (cash and chit)
 done

so:

1ath51atics
mathematics

Unassigned digits available for z and q are 7 and 8.

7*8=56

  Posted by Charlie on 2014-12-15 13:47:25
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