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.
DefDbl AZ
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 20141112 15:27:36 