11–20 of 137 posts
An expert system answer (Prolog, CLIPS) would be cool to see here.
Using the clpb library [0]: solution([A1,A2,A3,A4,A5,A6]) :- sat(A1 =:= A2*A3*A4*A5*A6), sat(A2 =:= ~(A3+A4+A5+A6)), sat(A3 =:= A1*A2), sat(A4 =:= A1+A2+A3), sat(A5 =:= ~(A1+A2+A3+A4)), sat(A6 =:= ~(A1+A2+A3+A4+A5)). [0] https://www.metalevel.at/prolog/puzzles
h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) )
h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) )
h52::noneabove.3 |- ( ch ( ph /\ ps ) )
h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) )
h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) )
h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /\ -. ta ) ) )
56:50:simprbi |- ( ph -> ( ta /\ et ) ) 57:56:simprd |- ( ph -> et ) 58:51:simp3bi |- ( ps -> -. et ) 59:57,58:anim12i |- ( ( ph /\ ps ) -> ( et /\ -. et ) ) 60::pm3.24 |- -. ( et /\ -. et ) 61:60,59:mto |- -. ( ph /\ ps ) 62:61,52:mtbir |- -. ch 63:50:simplbi |- ( ph -> ( ps /\ ch /\ th ) ) 64:63:simp2d |- ( ph -> ch ) 65:62,64:mto |- -. ph 66::3ioran |- ( -. ( ph \/ ps \/ ch ) ( -. ph /\ -. ps /\ -. ch ) ) 67:53:notbii |- ( -. th -. ( ph \/ ps \/ ch ) ) 68:67,66:bitri |- ( -. th ( -. ph /\ -. ps /\ -. ch ) ) 69:68:anbi1i |- ( ( -. th /\ -. th ) ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) ) 70::pm4.24 |- ( -. th ( -. th /\ -. th ) ) 71:69,70,54:3bitr4i |- ( -. th ta ) 72::nbbn |- ( ( -. th ta ) -. ( th ta ) ) 73:71,72:mpbi |- -. ( th ta ) 74::df-xor |- ( ( th \/_ ta ) -. ( th ta ) ) 75:73,74:mpbir |- ( th \/_ ta ) 76::xoror |- ( ( th \/_ ta ) -> ( th \/ ta ) ) 77:75,76:ax-mp |- ( th \/ ta ) 78:55:simprbi |- ( et -> ( -. th /\ -. ta ) ) 79::pm4.56 |- ( ( -. th /\ -. ta ) -. ( th \/ ta ) ) 80:78,79:sylib |- ( et -> -. ( th \/ ta ) ) 81:77,80:mt2 |- -. et 82:51:simp2bi |- ( ps -> ( -. th /\ -. ta ) ) 83::pm4.56 |- ( ( -. th /\ -. ta ) -. ( th \/ ta ) ) 84:82,83:sylib |- ( ps -> -. ( th \/ ta ) ) 85:77,84:mt2 |- -. ps 86:65,85,62:3pm3.2ni |- -. ( ph \/ ps \/ ch ) 87:86,53:mtbir |- -. th 88:87,75:mtpxor |- ta 89:65,85,62:3pm3.2i |- ( -. ph /\ -. ps /\ -. ch ) 90:89,87:pm3.2i |- ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th )
qed:90,88,81:3pm3.2i |- ( ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) /\ ta /\ -. et )
$= ( w3a simprbi mto wn wa mtbir wb sylib mt2 3pm3.2i pm3.24 simprd simp2d simp3bi anim12i simplbi wo notbii 3ioran bitri anbi1i wxo w3o pm4.24 3bitr4i nbbn mpbi df-xor mpbir xoror ax-mp simp2bi pm4.56 3pm3.2ni pm3.2i mtpxor )
ANZBNZCNZKZDNZOZEFNZVLVMVIVJVKACC ABOZVPFVOOFUBAFBVOAEFABCDKZEFOZGLUCBVKVMENOZVOHUFUGMIPZABCDAVQVRG UHUDMZBDEUIZDEUNZWBWCDEQNZVMEQWDVMVMOVNVMEVMVLVMVMABCUOZNVLDWEJUJ ABCUKULUMVMUPUAUQDEURUSDEUTVAZDEVBVCZBVSWBNZBVKVSVOHVDDEVEZRSZVTT DWEABCWAWJVTVFJPZVGDEWKWFVHFWBWGFVSWHFVLVSUELWIRST $. $)
An expert system answer (Prolog, CLIPS) would be cool to see here.
Using the clpb library [0]: solution([A1,A2,A3,A4,A5,A6]) :- sat(A1 =:= A2*A3*A4*A5*A6), sat(A2 =:= ~(A3+A4+A5+A6)), sat(A3 =:= A1*A2), sat(A4 =:= A1+A2+A3), sat(A5 =:= ~(A1+A2+A3+A4)), sat(A6 =:= ~(A1+A2+A3+A4+A5)). [0] https://www.metalevel.at/prolog/puzzles
Only the 5th is true, Metamath: $( THEOREM=noneabove LOC_AFTER=? h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) ) h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) ) h52::noneabove.3 |- ( ch ( ph /\ ps ) ) h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) ) h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) ) h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /…
It seems that 5 is a winner, as stated in the accepted answer. That's a pity, first I thought the goal of the question was to create an instance of Yablo's Paradox. Yablo's paradox is important because you cannot just argue that the paradox arises from an obviously incorrect definition, as people sometimes do for classical semantic paradoxes.
Only the 5th is true, Metamath: $( THEOREM=noneabove LOC_AFTER=? h50::noneabove.1 |- ( ph ( ( ps /\ ch /\ th ) /\ ( ta /\ et ) ) ) h51::noneabove.2 |- ( ps ( -. ch /\ ( -. th /\ -. ta ) /\ -. et ) ) h52::noneabove.3 |- ( ch ( ph /\ ps ) ) h53::noneabove.4 |- ( th ( ph \/ ps \/ ch ) ) h54::noneabove.5 |- ( ta ( ( -. ph /\ -. ps /\ -. ch ) /\ -. th ) ) h55::noneabove.6 |- ( et ( ( -. ph /\ -. ps /\ -. ch ) /\ ( -. th /…
Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct?
A) 25%
B) 50%
C) 60%
D) 25%5 and 6 are the only possible. But if 5 is true then 6 is false
None of the above can be true only with "more than one of the above (but different than all, none or one)", but then we would not be talking about the correct answer. It is assumed than only an answer can be correct.
I suppose than 6 then.
Updated: you are right, 6 can't be true, is the 5
Similar one I enjoyed in the Naive Bayes article from yesterday https://blog.floydhub.com/naive-bayes-for-machine-learning/ Multiple Choice: If you choose an answer to this question at random, what is the chance you will be correct? A) 25% B) 50% C) 60% D) 25%
Now, what would be the answer to the same question with the answer options:
A) 20%
B) 40%
C) 60%
D) 20%
E) 0%
6 can not be true because if it where then 1,2,3,4 & 5 would be false, but that would make 5 true as well which is a contradiction, therefore 6 can only be false 1 Can not be true because we just determined 6 as false so 1 can only be false 3 can not be true because we just determined 1 as false so 3 can only be false With 1 and 3 now proven false, 2 can only be true if 4 is false, but if 2 is true then 4 would be tr…
But the question doesn't ask about that. It just asks "which of these is the correct answer to this question?" There are no stated criteria for being the correct answer, and there is no reason to assume that the correct answer must be true or even capable of being true.
Consider this other question:
Which of the following is the correct answer to this question?
(A) This one.
(B) This one.