HawkMan

So by your logic, Everton now top of the EPL are just king of cheaters. How many of their goals have come from cheating. Who knows, who cares ? No point caring if Everton or anyone else is top.

Ship Of Theseus. Ancient Greek mariner Theseus has a ship made entirely of wooden planks, except sails etc. As each plank gets old he replaces it with a new plank. The old planks are stored in a warehouse. One by one he replaces the planks, all the time he has a sea worthy vessel. Eventually all the planks are replaced . Call this the Renovated Ship. Question is is this still the Ship Of Theseus, with no original plank. Now suppose he goes to the warehouse and rebuilds the ship using the original planks, call this the Reconstructed Ship. Which is the Ship of Theseus, the Reconstructed or Renovated? The Reconstructed has the original planks, the Renovated has a continuous timeline of existence back to the original. This is the puzzle of the Metaphysics of Identity. See vid for more.

Without rereading Cantor's arguments, which I did years ago, I'd say members of an infinite set are uncountable, hence Infinite, so one infinite set having more members is contradictory. It isn't as if one set reaches infinite first, there is no X marks the spot, reach this and it's infinite . Anyway let's not start on sets or we'll end up asking stuff like is the set of non self membered sets itself a member of it's own set. If it is a member of it's own set it's self membered so it isn't , and if it isn't a member of it's own set it's non self membered therefore it is. No let's not go there.

Both the hare and balls puzzle play on people's misconceptions about infinity. Infinity isn't just trillions and trillions and trillions, infinity is an abstract concept like zero. You can't have half of zero, or different size infinities. So, the balls; there are three possible answers, all plausible. 1. All the balls are thrown in and out before noon, so noon is actually outside the scope of he puzzle, so how many at noon is indeterminate. However if you really could throw an INFINITE number of balls in, then either they'll be an infinite number in the room at noon or NONE AT ALL, because an infinite number would have been thrown out. Half the number are thrown out, but half of infinity is a meaningless concept. The set up of the puzzle itself is impossible. As for the hare, this deals with infinity too. It wasn't until the 18th century that mathematicians realised that the sum of an infinite series could be finite. Draw a line on a piece of paper, that is a finite length, say 12 inches, and it can be divided infinitely many times. A half plus a quarter, plus an eighth plus a sixteenth etc to infinity still equals one. So the hare completes the task of reaching an infinite number of points between him and the tortoise in a finite time and overtake him. This is the book I got some of these from recommended .

43. 36 sheets make 36 products. 36 bits left over make another 6 sheets and 6more products , and 6 left over bits make another sheet to make 36 +6+1=43.

Correct. The trick of the puzzle is confusing first flag with start

Is it 12.5 seconds? 1st to 8th is 7 flags in 8 seconds is I.142 per flag times 11 .However the speed he ran from start to first isn't stated.

You place the object in the box and lock it with a lock that your friend can't open. Send it to your friend, who can't open it, but puts another lock on it, and sends it back. When getting it back you remove your lock and send it back again. It will then have only your friend's lock on it.

In 1899 at the race meet at Wolverhampton.

Very impressive! Correct . If the statement is false then it's false he'll be thrown in . The Tortoise and the Hare. This puzzle is attributed to Zeno of ancient Athens. A tortoise and a hare are in a race. The hare gives the tortoise a head start. The race starts, first the hare has to reach where the tortoise started, call that point T1, the tortoise has now moved to T2, the hare reaches T2, but the tortoise is now at T3, and so on, each time the gap is smaller but the tortoise continues to T4,5,6 etc. The hare has to cover each of these points, and the tortoise has always moved on, so cannot be caught. So a faster runner cannot overtake a slower one. Something is very wrong with this reasoning, but what.? Work this out and the numbered balls puzzle is worked out too.

" true" isn't saying anything, or could be construed as " I am saying true" which is self referential. Socrates can say something that even if its false will not put him in the river.

No, that is not logically true, in other words something that cannot be not true. Also mathematical statements are ruled out, such as 2+2=4. I know, Plato is such a grouch !

One minute before noon , you have an INFINITE number of ping pong balls outside a room, all numbered . You throw in balls 1 +2, immediately ball 1 is thrown back out. Half a minute before noon 3+4 are thrown in and number 2 thrown out. At a quarter of a minute to noon balls 5+6 are thrown in and number 3 is thrown out. At an eighth of a minute to noon 7+8 in and 4 out ad infinitum.... How many balls are in the room at Noon ?

Correct, in every sense.

Light bulb problem- clue - the room has furniture in it.

The Lord Plato is guarding a bridge over a river when Socrates appears. Socrates begs to be allowed passage. Plato bellows " If the next thing you say is true I will allow passage, but if the next thing you say is false I will throw you in the water, self referential statements like " I like potatoes, or my name is Socrates don't count, nor do statements like ,grass is green, it must be irrefutable provable and logically true" Socrates being clever says; " You will throw me in the water" If Plato does indeed throw Socrates in the water, then Socrates spoke truly and shouldn't have been thrown in, but if he doesn't throw him in, Socrates spoke falsely and should have gone in! Either way Plato is stuffed!! But hang on, Plato cannot fulfil his promise, it's logically impossible, so he has no obligation to keep his promise, and assuming free will can throw Socrates in the river if he pleases. It is argued that statements about future intentions cannot have a truth or false value. Socrates saying " You will throw me in the water " is neither true or false. However Socrates could have said something avoiding future dependant language that would have avoided a dowsing in the river. What?

No.

The simplest answer is that at the time the Lawyer instigated the lawsuit the Student hasn't won a case, so his case is thrown out. The Student has now won a case, and a second lawsuit instigated by the Lawyer will surely succeed.

Outside a room on the wall are three numbered light switches that operate three light bulbs inside the room. The door is solid with no window in it. Is it possible to identify which switch operates each bulb ? You may only enter the room ONCE after doing whatever you want with the switches and you can only touch TWO of the three switches. You are accompanying a lion and a goat on a journey , also you have a huge cabbage. You come to a river and see a rowing boat moored ready for use. However you can only take across one animal at a time, or indeed the cabbage. The boat is only big enough to carry you and one of the other three. You must get all three across one at a time, HOWEVER, if you leave the lion alone with the goat it will eat it, also if you leave the goat with the cabbage it will eat it. How can you get all three across safely, remembering that you have to be on board the boat each time you cross the river, either alone, or along with one animal or the cabbage. You can cross the river any number of times. PRISONER HAT PUZZLE.

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A thread for any logical puzzles or paradoxes you want to try out on others. Paradoxes are fun, if a bit philosophical. Here's a few to start. The Sheriff of Tombstone Arizona rides into town on thursday, opens his office up, he has a bed in there and only stays in town for one night. But when he leaves it's Sunday. How come? Two guys are in a restaurant, at the end of the meal the waiter gives them the bill, for £30. The internet is down, so they have to pay cash. Each has exactly £15 only on them...luckily. The waiter takes the money and hands it to the manager who is working the till. The manager examines the bill and says the bill is for £27 only, and instructs the waiter to.hand back £3. On his way back to the men he decides to pocket £1, and tell the men the bill cost £28. The two men leave with their £1 each. They both entered with £15, and left with £1 ,spending £14 each which equals £28, plus the £1 the waiter pilfered equals £29. Who has the missing pound ? THE GOD /BOULDER PARADOX. God by definition can do anything, nothing is beyond such a being. Can God create a boulder so heavy that He cannot lift it? If he can, then there's something he cannot do ie lift the boulder, if he can't then there's something he cannot do . Either way the definition of God is in trouble. THE LAWYER/STUDENT PUZZLE A lawyer helps a student qualify to become a lawyer, but generously waives his fee, for now. The student will pay the tuition fee when he has won his first case. Months go by and the student , now qualified, hasn't taken up a single case. The Lawyer anxious for his fee sues the Student , reasoning that if the court finds for him,he has won his case, and if he loses then the Student has won a case, either way the Student must pay up. The Student reasons that if the court finds for the tutor, he has lost and needn't pay, and if he wins then the tutor's case is thrown out and he still needn't pay. Who is right, what should the court do?

No complaints about today's EPL matches. Leeds yeah! Manchester United

Glass half empty. Glass half full - Burnley, remarkable job by Sean Dyche, Everton, James Rodriguez signing, good few years for Fleetwood, Accrington and Salford . Though I don't expect the Neville brothers to be smiling at 10.15 tonight.

You can get into a hell of a lot of linguistic tangle talking about Batman and Spiderman.

Havertz and Werner in the Chelsea line up at Brighton tonight. Looking forward to watching this and I'm not a Chelsea fan. New talent in EPL, fantastic. Sorry for this post, I'm unusual on this thread, a footy fan who actually likes watching the EPL, weird or what?