Little Silver Dagger (The Edwin Cross Files Book 1)

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Hence A is a knave and B is a knight. If they are both knights, then they will both answer "Yes. The vital clue I gave you was that the man was lazily lying in the sun. From this it follows that he was lying in the sun. From this it follows that he was lying, hence he is a knave.

So his name is Edwin. To begin with, A cannot be a knight, because a knight would never say that he is normal. So A is a knave or is normal. Suppose A were normal. Then B' s statement would be true, hence B is a knight or a normal, but B can't be normal since A is , so B is a knight.

This leaves C a knave. But a knave cannot say that he is not normal because a knave really isn't normal , so we have a contradiction. Therefore A cannot be normal. Hence A is a knave. Then B' s statement is false, so B must be normal he can't be a knave since A is. Thus A is the knave, B is the normal one, hence C is the knight. The interesting thing about this problem is that it is im- possible to know whether it is A who is telling the truth but isn't a knight or whether it is B who is telling the truth but isn't a knight; all we can prove is that at least one of them has that property.

Either A is telling the truth or he isn't. We shall prove: 1 If he is, then A is telling the truth but isn't a knight; 2 If he isn't, then B is telling the truth but isn't a knight. Then B really is a knight. Thus if A is telling the truth then A is a person who is telling the truth but isn't a knight. Then B isn't a knight. But B must be telling the truth, since A can't be a knight because A is not telling the truth. So in this case B is telling the truth but isn't a knight.

We shall show that if B is telling the truth then he isn't a knight, and if he isn't telling the truth then A is lying but isn't a knave. Then A is a knave, hence A is certainly not telling the truth, hence B is not a knight. Then A is not really a knave. But A is certainly lying about B, because B can't be a knight if he isn't telling the truth. So in this case, A is lying but isn't a knave. To begin with, A can't be a knight, because it can't be true that a knight is of lower rank than anyone else.

Now, suppose A is a knave. Then his statement is false, hence he is not of lower rank than B. So if A is a knave, so is B. But this is impossible because B is contradicting A, and two contradictory claims can't both be false. Therefore the assumption that A is a knave leads to a contradiction. Therefore A is not a knave. Hence A must be normal. Now, what about B? Well, if he were a knight, then A being normal actually would be of lower rank than B, hence A's statement would be true, hence B's statement false, and we would have the impossibility of a knight making a false statement.

Thus B is not a knight. Suppose B were a knave. Then A's statement would be false, hence B's would be true, and we would have a knave making a true statement. Therefore B can't be a knave either. Hence B is normal. Thus A and B are both normal. So also, A's statement is false and B's statement is true. So the problem admits of a complete solution.

Well, if A is a knight then B really is of higher rank than C, hence B must be normal and C must be a knave. So in this case, C is not normal. Suppose A is a knave. Then B is not really of higher rank than C, hence B is of lower rank, so B must be normal and C must be a knight. So in this case, C again is not normal. The third possible case is that A is normal, in which case C certainly isn't since only one of A, B, C is normal. Thus C is not normal. Step 2: By similar reasoning, it follows from B ' s state- ment that A is not normal. Thus neither A nor C is normal.

Therefore B is normal. Step 3: Since C is not normal, then he is a knight or a knave. Then A is a knave since B is normal hence B is of higher rank than A. So C, being a knight, would truthfully answer, "B is of higher rank. Then C, being a knave, would lie and say, "B is of higher rank than A.

A cannot be a knave, because then his wife would be a knight and hence not normal, so Mr. A's statement would have been true. Similarly Mrs. A cannot be a knave. There- fore neither is a knight either or the spouse would then be a knave , so they are both normal and both lying. For the second problem, the answer is the same. It turns out that all four are normal, and all three state- ments are lies.

First of all, Mrs. B must be normal, for if she were a knight her husband would be a knave, hence she wouldn't have lied and said he was a knight. If she were a knave, her husband would be a knight, but then she wouldn't have told the truth about this. Therefore Mrs. B is normal.

Hence also Mr. This means that Mr. A were both lying. Therefore neither one is a knight, and they can' t both be knaves, so they are both normal. She often forgot her name, and the one thing she was most likely to forget was the day of the week. Now, the Lion and the Unicorn were frequent visitors to the forest. These two are strange creatures. The Lion lies on Mondays, Tuesdays, and Wed- nesdays and tells the truth on the other days of the week.

The Unicorn, on the other hand, lies on Thursdays, Fri- days, and Saturdays, but tells the truth on the other days of the week, 47 One day Alice met the Lion and the Unicom resting under a tree. They made the following statements: Lion I Yesterday was one of my lying days. Unicorn I Yesterday was one of my lying days too. From these two statements, Alice who was a very bright girl was able to deduce the day of the week.

What day was it? He made the following two statements: 1 I lied yesterday. What day of the week was it? They were elsewhere, busily fighting for the crown. However, Tweedledum and Tweedledee were fre- quent visitors to the forest. Now, one of the two is like the Lion, lying on Mondays, Tuesdays, and Wednesdays and telling the truth on the other days of the week. The other one is like the Unicorn; he lies on Thursdays, Fridays, and Saturdays but tells the truth the other days of the week. To make matters worse, the brothers looked so much alike, that Alice could not even tell them apart except when they wore their embroidered collars, which they seldom did.

Thus poor Alice found the situation most confusing indeed!

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Now, here are some of Alice's adventures with Tweedledum and Tweedledee. Second One I I'm Tweedledee. Which one was really Tweedledum and which one was Tweedledee? Which was which? On another occasion, Alice met the two brothers, and asked one of them, "Do you lie on Sundays? What did he answer? Second One I I will lie tomorrow. He made the following statement: "I am lying today and I am Tweedledee.

One day Alice came across both brothers. Is it possible to determine who is who? Is it possible to determine the day of the week? A Mystery Resolved! On this great occasion, Alice resolved three grand mys- teries. She came across the two brothers grinning under a tree. She hoped that on this encounter she would find out three things: 1 the day of the week; 2 which of the two was Tweedledum; 3 whether Tweedledum was like the Lion or the Unicorn in his lying habits a fact she had long desired to know!

Second One I In fact, today is Monday. First One I Tomorrow is one of Tweedledee's lying days. Second One I The Lion lied yesterday. Alice clapped her hands in joy. The problem was now com- pletely solved. What is the solution? Just then flew down a monstrous crow, As black as a tar- barrel, Which frightened both the heroes so They quite forgot their quarrel. Doesn't it look as good as new? Even a baby couldn't tell the difference. Of course a baby couldn't tell the difference — one would hardly ex- pect a baby to do that!

The important thing is to restore the rattle to its rightful owner. Will you please do this for me? Therefore Tweedledum did indeed say that Tweedledee had spoiled his rattle. But because Tweedledum said it, it does not mean that it is necessarily true. Perhaps Tweedledum said it on one of his lying days.

Indeed, for all I know, it may be the other way around — maybe it was Tweedledum who spoiled Tweedle- dee's new rattle. Now all my good intentions are wasted. Now I shall tell you of Alice's actual adventures with the rattle. To her great delight, she suddenly came across both of them grinning under a tree. She went to the first one and sternly said: "I want the truth now! Who really owns the rattle?

To whom should Alice give the rattle? Alice restored the rattle to its rightful owner. Several days later, the other brother broke the rattle again. This time, no black crow came to frighten the brothers, so they began slamming and banging away at each other. Alice picked up the broken rattle and ran out of the forest as fast as she could. Some time later, she again came across the White King. She thoroughly explained the situation to him. Alice went trepidly into the forest, fearing that the battle might still be on.

As a matter of fact, the brothers had called a temporary truce, and Alice came across just one of them resting wearily under a tree. Alice went over to him and asked, "Who really owns this rattle? She asked the same question, and the reply was, "The owner of this rattle is telling the truth today. Alice asked the first one, "Do you own this rattle? Did Alice give the rattle to the first or the second one? Most people don't know it, but Tweedledee and Tweedledum actually have a third brother — his name is Tweedledoo.

He lives in a far-off land but occasionally comes around to these parts. He looks as much like Tweedledee and Twee- dledum as Tweedledee and Tweedledum look like each other. For one thing, the possibility that there really was a third one would mean that all her past inferences were invalidated, and that she really may not have figured out the day of the week when she thought she had.

Of even greater practical im- portance, she may not have restored the rattle to its rightful owner after all. Alice pondered deeply over these troublesome thoughts Finally, she asked Humpty Dumpty a sensible question. Alice walked away in troubled silence. There are four different accounts of just what hap- pened next, and I shall tell you all of them. I ask the reader to assume two things: 1 if there really is an individual other than Tweedledee or Tweedledum who looks indistin- guishable from them, then his name really is Tweedledoo; 2 if such an individual exists, then he really does lie all the time.

I might remark that the second assumption is not necessary for the solution of the next mystery, but it is for the two which follow after that. The First Version. Alice came across just one brother alone in the forest. At least, he looked like he was Tweedledee or Tweedledum. The Second Version. According to this version, Alice came across what seemed to be both brothers.

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She asked the first one: "Who really are you? The Third Version. According to this version, Alice came across just one of them. He made the following statement: "Today is one of my lying days. The Fourth Version. She asked, "Does Tweedledoo really exist? Second One I I exist. What do you make of this version? How come four versions? Well, to tell you the truth, I didn't invent these stories myself; I heard them all from the mouth of the Jabber- wocky. Now, the conversation between Alice and Humpty Dumpty really happened: Alice told me this herself, and Alice is always truthful.

But the four versions of what hap- pened after that were all told to me by the Jabberwocky. Now, I know that the Jabberwocky lies on the same days as the Lion Monday, Tuesday, Wednesday and he told me these stories on four consecutive weekdays. I know they were weekdays, because I am lazy and sleep all day Sat- urdays and Sundays. They were told to me in the same order as I recounted them. From this information, the reader should have no dif- ficulty in ascertaining whether Tweedledoo really exists or whether Humpty Dumpty was lying.

Does Alice know whether Tweedledoo exists? The only days the Unicorn can say "I lied yesterday" are Thursdays and Sundays. There- fore the only day they can both say that is on Thursday. The lion's first statement implies that it is Monday or Thursday. The second statement implies that it is not Thursday.

Hence it is Monday. On no day of the week is this possible! So there is no day he could say both. It well illustrates the difference between making two statements separately and making one statement which is the conjunction of the two. Indeed, given any two statements X, Y, if the single statement "X and Y" is true, then it of course follows that X, Y are true separately; but if the conjunction 11 X and Y" is false, it only follows that at least one of them is false.

Now, the only day of the week it could be true that the Lion lied yesterday and will lie again tomorrow is Tuesday this is the one and only day which occurs between two of the Lion's lying days. So the day the Lion said that couldn't be Tuesday, for on Tuesdays that statement is true, but the Lion doesn't make true statements on Tues- days. Therefore it is not Tuesday, hence the Lion's state- ment is false, so the Lion is lying. Therefore the day must be either Monday or Wednesday.

If the first statement is false, then the first one is actually Tweedledee and the second one is Tweedledum, and hence the second statement is also false. Therefore either both statements are true or both statements are false. They can't both be false, since the brothers never lie on the same day. Therefore both state- ments must be true.

So the first one is Tweedledum and the second one is Tweedledee. Also, the day of the encounter must be Sunday. The second one's statement is certainly true. Now, we are given that the day of the weekis different from that of the last problem, soitis a weekday. Therefore it cannot be that b oth statements are true, so the first one must be false. Therefore the first one is Tweedledee and the second is Tweedledum. Therefore the other one must have answered truthfully and said "No.

Therefore the first one does not lie on Saturdays, so the second one lies on Saturdays. The second one is telling the truth on this day since the first one is lying , so it is now Monday, Tuesday, or Wednesday. The only one of these days in which it is true that he will lie tomorrow is Wednes- day. So the day is Wednesday. His statement is certainly false for if it were true, then he would be lying today, which is a contradiction.

Therefore at least one of the two clauses "I am lying today," "I am Tweedledee" must be false. The first clause "I am lying today" is true, therefore the second clause must be false. So he is Tweedledum. Therefore he is telling the truth today. So his statement is true: either he is lying today or he is Tweedledee. Since he is not lying today, then he is Tweedledee. Both statements are obviously true, so it is a Sunday.

It is not possible to determine who is who. Therefore today cannot be Sunday. So the first one is telling the truth, and since it is not Sunday , the second one is therefore lying today. The second one says today is Monday, but he is lying, so it is not Monday either. Now, the second one has also told the lie that the Lion lied yesterday, hence yesterday was really one of the Lion's truthful days. We have already ruled out Sunday and Monday, so today must be Friday or Saturday. Next we observe that tomorrow is one of Tweedle- dee' s lying days since the first one, who is speaking the truth, said so.

Therefore today cannot be Saturday. Hence today is Friday. From this it further follows that Tweedledee lies on Saturdays, hence he is like the Unicorn. Also, the first one is telling the truth today, which is a Friday, hence he is Tweedledum. This proves everything. Suppose the first one told the truth. Then the rattle belongs to Tweedledee. Hence the first speaker is Tweedledee and should get the rattle. Suppose the first one lied. Then the rattle belongs to Tweedledum. Then also the second one told the truth so is really Tweedledee.

Then again the first one owns the rattle. So in either case, the rattle belongs to the first speaker. Suppose his statement is true. Then the owner of the rattle is lying today, hence cannot be the speaker. Suppose on the other hand that his statement is false. Then the owner of the rattle is telling the truth today, hence again cannot be the speaker. Humpty Dumpty was right!

Suppose the speaker is lying. Then the owner of the rattle is not telling the truth today; he is lying today, hence must be the speaker. But suppose the speaker is telling the truth. Then the owner of the rattle is indeed telling the truth today. If it is a weekday, then he must be the owner, but if it is a Sunday, then both brothers are telling the truth today, so either could be the owner. In summary, if it is a weekday, then the speaker is defi- nately the owner.

If it is Sunday, then the chances are even that he is the owner. Therefore the chances are 6V2 out of 7 — or 13 out of 14 — that he is the owner. The clue here is that Alice did know who to give it to. Had the second one answered "Yes," then one of them would have been telling the truth and the other lying, hence Alice would have no way of knowing who owned the rattle. But I told you she did know, hence the second one didn't answer "Yes. So Alice gave it to the first one. The speaker claimed that the following statements are both true: 1 He is either Tweedledee or Tweedledum 2 He is lying today.

If his claim were true, then 1 and 2 would both be true, hence 2 would be true, which would be a contradiction. Therefore his claim is false, so 1 and 2 cannot both be true. Now, 2 is true since his claim on this day is false , so it must be 1 that is not true. Therefore he is neither Tweedledee nor Tweedledum, so he must be Tweedledoo.

Then the second one is also lying. If the second one were Tweedledee or Tweedledum, then Tweedledee and Tweedledum would be lying on the same day, which is im- possible. Therefore the second one must be Tweedledoo. I think Descartes pointed out that anyone who says he exists is making a true statement; certainly I have never met anyone who didn't exist. Since the second statement is true and it is not Sunday, then the first statement must be false.

Solution to the Epilogue. The third version of the story is definitely false. Also none of the stories was told on a Saturday or Sunday. The only way these four stories can be fitted into four consecutive days satisfying these conditions is that the third version was told on a Wednesday. So the last version was told on a Thursday, hence must be the true one.

So Tweedledoo doesn't really exist! I'm quite sure, incidentally, that had Tweedledoo really existed, Lewis Carroll wouldhave known about it. As for Alice, since the fourth version is the only one which really took place, then Alice should have no difficulty in realizing that all these "Tweedledoo fears" were ground- less. The suitor was to choose one of the caskets, and if he was lucky enough or wise enough to choose the one with the portrait, then he could claim Portia as his bride.

On the lid of each casket was an inscription to help the suitor choose wisely. Now, suppose Portia wished to choose her husband not on the basis of virtue, but simply on the basis of in- telligence. She had the following inscriptions put on the caskets. Which casket should the suitor choose? Portia's suitor chose correctly, so they married and lived quite happily — at least for a while.

Then, one day, Portia had the following thoughts: "Though my husband showed some intelligence in choosing the right casket, the problem wasn't really that difficult. Surely, I could have made the problem harder and gotten a really clever husband. Which casket contains the portrait? Epilogue As fate would have it, the first suitor turned out to be Portia's ex-husband.

He was really quite bright enough to figure out this problem too. So they were remarried. The husband took Portia home, turned her over his knee, gave her a good sound spanking, and Portia never had any foolish ideas again. They had a daughter Portia II — henceforth to be called "Portia. She also decided to select her husband by the casket method.

The suitor had to pass two tests in order to win her. The First Test. In this test each lid contained two statements, and Portia explained that no lid contained more than one false statement. The Second Test. If the suitor passed the first test, he was taken into another room in which there were three more caskets. Again each casket had two sentences inscribed on the lid. Portia ex- plained that on one of the lids, both statements were true; on another, both statements were false; and on the third, one statement was true and one was false.

They lived happily ever after and had a lovely daughter Portia III — henceforth to be called "Portia. She also decided to choose her husband by the casket method. The suitor had to pass three tests in order to win her! The tests were quite ingenious. She went back to her grandmother's idea of having only one state- ment inscribed on each casket rather than two. But she introduced the following new wrinkle: She explained to the suitor that each casket was fashioned by one of two famous Florentine craftsmen — Cellini or Bellini. Whenever Cellini fashioned a casket, he always put a false inscription on it, whereas Bellini put only true inscriptions on his caskets.

In this unusual test the suitor if he guessed blindly would have a two out of three rather than a one out of three chance. Instead of using a portrait, Portia used a dagger which was placed in one of the three caskets; the other two caskets were empty. If the suitor could avoid the casket with the dagger, then he could take the next test. In this test, the suitor's chances if he guessed blindly were one out of two. Portia used only two caskets, gold and silver, and one of them contained her portrait no dagger was used in this test.

Again each casket was fashioned either by Cellini or Bellini. The Third Test If the suitor passed these two tests, he was led into another room containing a gold, silver, and lead casket. Again, each casket was fashioned by either Cellini or Bellini. Now in this test, the suitor's chances were one out of three if he guessed blindly ; Portia used a portrait of herself, and the portrait was in one of the caskets. To pass the test, the suitor had to 1 select the casket containing the portrait; 2 tell the maker of each casket.

The fourth and final tale is the most baffling of all, and it illustrates a logical principle of basic importance. The suitor of the last story passed all three tests and happily claimed Portia III as his bride. They had many children, great-grandchildren, etc. Several generations later a descendant was born in America who looked so much like the ancestral portraits that she was named Portia Nth — henceforth to be referred to as "Portia. In addition, she was highly vivacious and a bit on the mischievous side.

She also decided to select her hus- band by the casket method which was somewhat of an anomaly in modern New York, but let that pass. The test she used appeared simple enough; she had only two caskets, silver and gold, in one of which was Portia's portrait. The lids bore the following inscriptions: Gold Silver Which casket would you choose?

Well, the suitor reasoned as follows. If the statement on the silver casket is true, then it is the case that exactly one of the two statements is true. This means that the statement on the gold casket must be false. On the other hand, suppose the statement on the silver casket is false. Then it is not the case that exactly one of the statements is true; this means that the statements are either both true or both false.

They can't both be true under the assumption that the second is false , hence they are both false. So regardless of whether the statement on the silver casket is true or false, the statement on the gold casket must be false. Therefore the portrait must be in the gold casket.

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So the suitor triumphantly exclaimed, "The portrait must be in the gold casket" and opened the lid. To his utter horror the gold casket was empty! The suitor was stunned and claimed that Portia had deceived him. Sure enough, the portrait was there. Now, what on earth went wrong with the suitor's reasoning?

However, you seem like a very attractive young man, so I think I'll give you another chance. I really shouldn't do this, but I will! In fact, I'll forget the last test and give you a simpler one in which your chances of winning me will be two out of three rather than one out of two. It resembles one of the tests given by my ancestor Portia III.

Now surely you should be able to pass this one! That hardly qualifies as 'unappreciated' in my book. These titles have been reprinted ever since they were first published! I mean, come on people But there are lots of titles like this on the list, unfortunately. Time someone the list owner maybe cleaned up this list? Hard job though, I'll admit that. Aug 06, PM. I just deleted a bunch of bestsellers Since the description specifically says "not on any best seller lists"! More need to go but it's very time consuming Aug 07, AM.

For reference starting with Oprah, as per this list's express description a book "acclaimed by Oprah" has no place here , the books that made Oprah's original Book Club and Oprah's Book Club 2.

10 Terrific Facts About Stephen King

NY Times No. New York Times No. Clarke The Man from St. Auel Texas by James A. Salinger Caravans by James A. Marquand Return to Paradise by James A. Salinger The Robe by Lloyd C. Gann Beyond This Place by A. Pulham, Esquire by John P. Marquand Mr. Cronin The Robe by Lloyd C. Costain B. Costain Gentleman's Agreement by Laura Z. Shannon's Way by A.

Cronin My Son, My Son! Porter The Portygee by Joseph C. Lincoln The Great Impersonation by E. Hutchinson The Sheik by Edith M. Williamson and A. Locke T. Locke Felix O'Day by F. Porter Mr. Britling Sees It Through by H. Dell The U. Porter Greatheart by Ethel M. Hopkinson Smith Septimus by William J. Tolkien The Hobbit, J. Lewis She, H. White The Ginger Man, J. Carlson Who Moved My Cheese? Rowling Goosebumps, R. Lobstergirl wrote: "I just deleted a bunch of bestsellers Would by no means want to restrict the notion of "bestseller" to the lists specifically referenced here, though Earlier I removed all the Stieg Larsson books Aug 08, AM.

Lobstergirl wrote: "Earlier I removed all the Stieg Larsson books Winners of major awards can hardly be considered to have "flown under the radar" or be "unappreciated," either You Rock! Bettie wrote: "T:A Sweet Ladies! Martin Surviving the Applewhites by Stephanie S. Basil E. Frankweiler by E. Darwin L. Aug 08, PM. Stead, written by Philip C. Martin Luther King, Jr. Illustrated by David Small, written by Judith St. Johnson Zin! Belting Mr. Nicholas Mordvinoff ; text: Will, pseud. Seuss, pseud. Aug 28, PM. I feel like any book on this list that has over ratings, is probably not so "unappreciated" any more.

Aug 29, AM. Amber wrote: "I feel like any book on this list that has over ratings, is probably not so "unappreciated" any more. The threshold for GR's "Moderately Underrated" list is between 1, - 10, ratings. But with 5, ratings, you can certainly no longer say a book has "flown under the radar! Sep 25, PM.

Gee, folks, thanks for all of that research. It sure took a lot of the fun out of this list! Is it somehow disqualifying that a book that would get you puzzled looks in any bookstore in America was a best-seller in ? Does that make it overly appreciated in the here and now? Is it appreciated or underappreciated? My point is that 'underappreciated' is in the eye of the beholder.

We are, pretty much by definition, a group of avid readers. A book that receives 1, ratings here can still be underappreciated by the general public, which was my automatic, mental definition of the term when I selected my contributions to the list. I listed books that I - - my favorite critic, after all -- consider underappreciated. Go and set stringent limits for your definition of 'underappreicated' if you like, but I think that it will greatly reduce contributions to the list.

The value in a list like this is in giving a means to consider what might be on their personal TBR list. Limit the list and you limit its value. Oct 01, PM. Add a reference: Book Author. Search for a book to add a reference. We take abuse seriously in our discussion boards. Only flag comments that clearly need our attention.

We will not remove any content for bad language alone, or being critical of a particular book. Add books from: My Books or a Search. Friends Votes.

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How to Vote To vote on existing books from the list, beside each book there is a link vote for this book clicking it will add that book to your votes. Flag this list. Inappropriate The list including its title or description facilitates illegal activity, or contains hate speech or ad hominem attacks on a fellow Goodreads member or author.

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