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Survival Surmise (Posted on 2014-11-12) Difficulty: 3 of 5
1. Rocky the dog is alive.
2. Rocky the dog is dead.
3. Exactly one of statements 6 and 9 is true.
4. Exactly one of statements 2 and 6 is false.
5. Statements 4, 5 and 10 are all false.
6. Exactly one of statements 1 and 10 is false.
7. Exactly 5 statements are true.
8. Exactly one of statements 3 and 10 is false.
9. Exactly one of statements 6 and 10 is true.
10. Exactly one of statements 1 and 2 is false.
11. Statements 1, 8 and 11 are all false.

Which of the above statements are definitely true? Is Rocky the dog alive or dead?

*** Based on an original problem by Louise Mayor.

No Solution Yet Submitted by K Sengupta    
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Solution solution | Comment 1 of 2
DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 For t1 = 0 To 1
     t2 = 1 - t1
 For t3 = 0 To 1
 For t4 = 0 To 1
 For t5 = 0 To 1
 For t6 = 0 To 1
 For t7 = 0 To 1
 For t8 = 0 To 1
 For t9 = 0 To 1
 For t10 = 0 To 1
 For t11 = 0 To 1
   tot = t1 + t2 + t3 + t4 + t5 + t6 + t7 + t8 + t9 + t10 + t11
   good = 1
   If t3 <> Abs(t6 Xor t9) Then good = 0
   If t4 <> Abs(t2 Xor t6) Then good = 0
   If t5 <> Abs(t4 + t5 + t10 = 0) Then good = 0
   If t6 <> Abs(t1 Xor t10) Then good = 0
   If t7 <> Abs(tot = 5) Then good = 0
   If t8 <> Abs(t3 Xor t10) Then good = 0
   If t9 <> Abs(t6 Xor t10) Then good = 0
   If t10 <> Abs(t1 Xor t2) Then good = 0
   If t11 <> Abs(t1 + t8 + t11 = 0) Then good = 0
   
   If good Then
     Text1.Text = Text1.Text & t1 & t2 & t3 & t4 & t5 & t6 & t7 & t8 & t9 & t10 & t11 & crlf
   End If

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

finds

10100000110
10100010110

So either only statements 1, 3, 9 and 10 are true, or statement 7 is true also.  Either way, Rocky is alive, as that's said in statement 1.

Of course, this puzzle will exist long after Rocky has died and will still "prove" he's alive.  Such is the way with arguments dependent on metastatements. If statement 7 had referred to "exactly 4", there would have been a recognizable paradox, but since that didn't happen we imagine we have a proof of Rocky's continued living.

  Posted by Charlie on 2014-11-12 15:27:36
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