I find the language unclear in the context of a single-culprit case. Should I interpret PE’s statement as “culprit is not PE or DO” (analogous with HO’s)? That’s what I’m doing below.
PA: ¬DO
PE: culp PA, SH, IG, HO
SH: culp PA, SH, HO
IG: culp PA, SH, IG, DO, HO
DO: culp SH
HO: culp PA, PE, SH, HO
We start knowing there are 2-3 false statements and therefore 3-4 true.
Exactly one of PA and DO is true. So ignore them. In the remaining 4 we must have 1-2 false statements, and therefore 2-3 true.
Of the candidate culprits and ignoring the PA/DO statements, PA appears in 4, SH in 4, IG in 2, DO in 1, HO in 4. Only one of those gives 2-3 true statements, so IG did it. SH, DO and HO are lying.
Tried this before the clarification and was thrown by peacock’s statement, which I initially thought must be false (and meaningless) because there is only one suspect. But this led to at least two solutions or ambiguities, at which point I tried reading it as “neither… nor…”.
Iguana is the culprit, Shark, Dog and Horse are lying.
First test if dog is true. If shark is the culprit then shark, iguana and horse are true. Panther is false. Peacock is true (but false under my inital reading, which makes this a valid solution!), so there are not enough lies.
Therefore, panther is true and dog is false. If shark is true then horse and iguana are true. Peacock is also true (but false under my initial reading, which led to not enough information to distinguish between horse and panther as the culprit, at which point I started to be confused), so there are not enough lies.
Therefore, shark is false. If it is peacock or dog then peacock and iguana/horse would be false, which is too many lies, leaving only iguana.
I think I managed it in about 2:45 once I realised my initial mistake, and just barely scraped in under 5 minutes altogether.
The culprit is Iguana and the liars are Dog , Horse & Shark
How the statements relate:
Panther true → Dog false
Dog true → Panther false, Shark true
Peacock true → Iguana true
Shark true → Peacock true, Iguana true, Horse true
Horse true → …
Iguana true → …
So if Dog says the truth it follows that Shark, Peacock, Iguana and Horse also tell the truth. That would mean too few liars. So Dog is a and Panther is a
By similar reasoning Shark must also be
So the culprit is one of Peacock, Dog or Iguana
Only 1 more lie is possible. So both Iguana and Peacock since their statements are related.
That leaves only 1 suspect: Iguana , as Peacock exonerates Dog and themselves: Iguana, and that means Horse is also
The puzzles are really cool and I am sorely out of practice
Don’t worry about it! The first time I tried one of the hardest puzzles, it took me so much longer than the listed target times to tease out all the bits of information that the listed targets seemed completely unreasonable to me. Later I re-did that same puzzle starting from a different conjecture, and discovered that the entire solution fell out in about 60 seconds. So tactical starting points can be a factor, but at the same time it’s not always apparent where to begin, so you might get an easy ride by chance some of the times, and a real slog at others. All of which is why I’ve made times a comparatively minor part of the score.
I’m trying different approaches as I go, and some fit much better than others. (I’d try a machine solution too, just to amuse myself, but I’d have to learn Prolog, and I don’t wanna.)
Ha! Yes, I too have been ignoring a little voice in my brain suggesting that this would be a fun reason to do some Prolog :). (I’m assuming that the designers did exactly that to establish and validate all of the case solutions, but I don’t know for sure.)
The commissioner looks pleased. “Well done everyone, our rating is up to 89%. There are only two cases left in this file, but you now have seven statements to consider! Good luck!”
Case 7/8, dossier 11.
Time brackets:
(a) <= 4 mins
(b) 4-6 mins
(c) 6-12 mins
(d) 12+ mins
(x) not using a timer
Culprits across the top, statements down the side.
PA
PE
SH
IG
DO
HO
BE
PA
PE
y
y
y
n
y
y
y
SH
y
n
y
n
y
y
y
IG
HO
n
y
n
y
n
y
n
DO
n
n
y
n
n
y
n
BE
y
y
n
y
y
n
n
ignoring PA/DO of which exactly 1 must be false, PE SH IG HO BE = 1 lie = 4 truths in the remaining 5.
Ignore IG for now, 3-4 truths in the remaining 4. That gives possible culprits
PA, PE, DO, HO at 3, and IG must be true to make it up to 4.
(edit to add the one I missed
if PA is culprit DO is false, PA is true, IG is false.
)
If PE is culprit PE is true, IG is false.
If DO is culprit DO is false, IG is true
If HO is culprit HO is true, IG is false
So DO is culprit. Checking all statements:
DO is false, so PA and IG are true.
PE is true, SH is true, HO is false, BE is true.
Falsity count is correct.
Panther and dog are a true/false pair and dog/bear are mutually exclusive (although they both could be lying).
If they are both lying then bear did it, but that makes horse false, which is too many lies.
If dog is telling the truth then panther and bear are lying and one of them must be the culprit per iguana’s statement. But neither is a herbivore, so horse would be false, which is too many lies.
So dog is lying, panther and bear are telling the truth.
Shark cannot be lying, becuase iguana and peacock must then be true, which contradicts iguana’s statement. So shark and peacock are true.
Horse is the only possible herbivore suspect left and is over 180cm tall, so they cannot be the culprit and are therefore the second lie, which means iguana is telling the truth, yielding dog as the liar who fits the other statements.
I found that one considerably easier than the last two, but maybe I just got lucky with my starting point.
Dog is the culprit and a liar The other liar is Horse
I tried assuming Dog was truthtelling but that would mean both Panther and Bear were liars immediately and so Shark and Horse would be the only suspects. But then Iguana would also be lying. That meant too many lies.
So Dog → Panther and Horse and Shark are
Next I assumed Shark might be a liar which would mean that either Peacock or Iguana would be the culprit. But with a second lie everyone else has to tell the truth which would make Iguana the suspect and make their claim another lie.
So Shark → Peacock and Iguana
With all herbivores → Horse
So if everyone else tells the truth, according to Iguana one of the liars must be the culprit. Since Horse was already proven too tall for Dog‘s lie… Dog is
and the liars are Dog 
, Horse 
