bonanova

Berry's Paradox enjoyed a nice discussion here a while back. Read about it and add more if you like. I'll leave this thread open.

LMMSOAT, EHCAW. ACASASDBHAFMMA. (16)JAJWUTHTFAPOW. JFDABHCAJCTA. (11)HDSOAW. HDHAGF. ATKHAATKMCPHTA. (12)

ILTSONITM. (13) GA, MMD. (12) IGMHAOHCR. (12) YCHTT! (11) WWGHIFTC. (12) MTFBWY. (8) T, IAFWNIKA. (13) YTTM? (10) R. (11) F, MD, IDGAD. (15)

SBR, AYL? ITL, SIG. ABS, WHT, WIAWW. (16) CROAOF. JFNAYN. YCBSBAC, AFDULE. (16) AIAM, NCFAB, TLLJLDHSH. TSITSLDWHL. TLLJAITH. (13) OTFDOC, MTLGTM: APIAPT. (24)

Warm-up. More challenging ones of the same genre to follow. WIYW? P, P, F, F. O, WARII. S! C! P! WANLS ... IHTBG. PATIYT. DLHWI. ITALAKOT.

Almost fished ... Three to go. A bad joke teller might receive this . . . Actor who once played a ButlerMove the tiniest iota . . . . . . . . . . .A dogs worst enemiesLike mosh pit dancers . . . . . . . . . . .A donation that cant be returnedKwame's superpower . . . . . . . . . . . . Disguises a box's contentsTravels from World 1 to World 4 . . . . . .Don't punishA Boolean value . . . . . . . . . . . . . .Evidence of needing a diaper changeWithout potty language or innuendo . . FanaticGives two thumbs up, perhaps . . . . . . . Get the code runningTime-bending video game from 2008 . . . . .Give the evil eyeGet up . . . . . . . . . . . . . . . . . . In need of an editorDon't agree to disagree . . . . . . . . . .It's straight from the horses mouth?Makes a sweater . . . . . . . . . . . . . .Negotiation bargaining chipYou might smear a shmear on one . . . . . .Renaissance fair weaponDeserve (as a reward) . . . . . . . . . . .Word with break or attackTurning point? . . . . . . . . . . . . . . You might need it if you're boring

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It's similar to bon-chan's approach of setting up a logical question that cannot be answered by a simple yes/no for one of the doors. I'm not sure he poofs for the left door. In your logic does F -> anything? I was not sure that he could not say Yes or No, with equal validity if it were the leftmost door. That is, A -> B can be taken to be ^A v B: F implies anything, and anything implies T. So for the leftmost door and A = "there is at least one door to the left of the correct door" your question is If A then are there 2 doors left of the correct door. A being false, can't the answer be Yes or No instead of "I can't answer because the premise is false"? The only approach is to force a Yes/No/Can't answer response, agreed. Explanation for F -> T to be legit: If 2+2=5 then New York is a small city. In every case where 2+2=5 New York is a small city. But there are no cases where 2+2=5. Thus: In no case is New York a small City. The only prohibited conditional is T -> F. the other three are OK. No?

I was thinking the latter... but since you mention it, let's analyze. Do any possible "false offers" from a lying tribesman result in a different approach? The only ways I can think for the offer itself to be a lie is if he will answer more than just one question (which only makes life easier), or will not answer any questions (which means you just have to guess), or will choose his answer from some other set of responses besides "Yes / No" (which I think would leave you with too little information to ask the right question). Any other options I missed? I would add to the list: Answer a different number of questions Or none at all Replies other than yes/no promise that his yes/no answer would be truthful may not be reliable. It was option 4 actually that came to my mind. But perhaps a liar lying about telling the truth and having to tell the truth for the false promise to be false cancels out. e.g. Both a T and a L will say "I am telling the truth;" neither can say "I am lying." It's probably the latter, and we are worrying about nothing.

Our approaches are often complementary. I'm not ready to say that I abhor calculus, but I am old (and tired) enough to call in transferable concepts where they apply if it avoids re-deriving a result. But, this afternoon I did the whole d/dx on this problem, but surrendered when I saw x4 and x3 terms. So I didn't derive x=40 that way, I got it numerically from my Newton-Raphson program, then plugged 40 into the stationary condition just to verify the approaches agree. I worked in optics long enough for Snell's law to have been like f = ma to me. It just shows the bend in light's path at interfaces that creates the least time path. Just as OP asks here. In optics it's refractive indices, in this puzzle it's running vs swimming, but it's the same effect. But my optics journey was 40 years ago and the connection didn't hit me at first. Full disclosure, Snell's law is an extension of the principle of least action, a fundamental underpinning in several disciplines. Long version of the answer to a question that wasn't asked...

A new approach. Works for me.

The solution has been given in the OP. Thread closed.

Maybe OP meant non-negative? I think I have a proof there is no other solution. Construct the table.

Here's an answer Nice.

Sometimes the fun part challenge is to find the shortest an intuitive path through the messy calculations. Y-san did the brute force calculation. I tried all the trig approaches until I rediscovered Snell's law (usually used for optics). It's a cute puzzle because it ends up with similar triangles on the sand and in the water. I don't know whether that was because the speed ratio was 2.

[spoiler='The answer I was looking for] [spoiler='If you are through looking for it']Would you agree that either the way home is the right door, or its the left door and you will answer no? If the right door leads home Hatter will say yes; if it's the middle door he'll say no, and he will disappear if it's the left door.

Should we take into account that his offer is not to be taken as reliable in the case that he is a liar? Or should we assume a trusted person tells us this person will truthfully or falsely answer a yes/no question if possible? I assume it's the latter, but the former would be interesting to analyze as well.