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Post by Flying Monkeys on Jan 1, 2018 18:54:16 GMT
Three squirrels are sitting on a board: The Squirrel King hands each squirrel a card, on which a number is written. The squirrels can read only the number on their own card. The King tells them: “Each card has a different number on it, and your card tells you the number of steps you are from the square with the Golden Acorn. Moving one square horizontally or vertically along the grid counts as a single step. No diagonal steps.” (So if the acorn was under Black, Black’s card would say 0, Grey’s would say 4, and Red’s 5. Also, the number of steps given means the shortest possible number of steps from each squirrel to the acorn.) The King asks them: “Do you know the square where the Golden Acorn is buried?” They all reply “no!” at once. Red then says: “Now I know!” Where is the Golden Acorn buried? Please PM me your answer, I'll let you know whether you are right on wrong on this thread. (note: for the purposes of today, squirrels can speak, hear, read, count and are perfect logicians. They can also move in any direction horizontally and vertically, not just the direction these cartoons are facing. They all can see where each other is standing, and the cells in the grid are to be considered squares.) |
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Post by drtokyo on Jan 1, 2018 19:38:05 GMT
Three squirrels are sitting on a board: The Squirrel King hands each squirrel a card, on which a number is written. The squirrels can read only the number on their own card. The King tells them: “Each card has a different number on it, and your card tells you the number of steps you are from the square with the Golden Acorn. Moving one square horizontally or vertically along the grid counts as a single step. No diagonal steps.” (So if the acorn was under Black, Black’s card would say 0, Grey’s would say 4, and Red’s 5. Also, the number of steps given means the shortest possible number of steps from each squirrel to the acorn.) The King asks them: “Do you know the square where the Golden Acorn is buried?” They all reply “no!” at once. Red then says: “Now I know!” Where is the Golden Acorn buried? Please PM me your answer, I'll let you know whether you are right on wrong on this thread. (note: for the purposes of today, squirrels can speak, hear, read, count and are perfect logicians. They can also move in any direction horizontally and vertically, not just the direction these cartoons are facing. They all can see where each other is standing, and the cells in the grid are to be considered squares.)It's under the Squirrel King. He's not giving out golden acorns to peons. |
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Post by Flying Monkeys on Jan 1, 2018 19:52:38 GMT
It's under the Squirrel King. He's not giving out golden acorns to peons. No. (Also, when replying, click below the quote box to separate your text from the quote.) |
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Post by drtokyo on Jan 1, 2018 20:06:55 GMT
Oops!
My guess is that it's under that square, the one I'm pointing at.
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Post by warlock on Jan 1, 2018 20:29:10 GMT
It certainly is not where any of them are standing and numerical elimination puts it.........
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Post by Flying Monkeys on Jan 1, 2018 21:12:05 GMT
Warlock and Bartlesby are both correct.
Well done!
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Post by Flying Monkeys on Jan 13, 2018 12:48:31 GMT
Here is the answer. I'll name cells in the format C3R4, meaning column 3 (from the left), row 4 (from the top).
What are the possible numbers that each card can say (i.e. how many squares can each squirrel move to)?
R can say 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
G can say 0, 1, 2, 3, 4, 5, 6, 7, 8
B can say 0, 1, 2, 3, 4, 5, 6, 7
Clearly no card says 0 as they would know straightaway.
Lets' focus on what red's card says. Key here is that he doesn't know immediately, but he does know when the other squirrels say they don't know. So we are looking for a situation where red's number allows him to immediately narrow it down to 1 free square and 1 or 2 occupied squares. When the squirrels say they don't know, the occupied squares are knocked out, leaving the 1 free square as the only possible option for red. Let's work through the possible options:
Could red's card say 9? No, if it did he would know where it was immediately (C1R6), because he's the only one that can move 9 squares by the most direct route.
Could red's card say 8? If it did, possible squares would be C1R5 and C2R6. But, C1R5 is 3 squares from both grey and black and everyone has a different number so that cannot be it. Which just leaves C2R6. I.e. if it 8, red would know immediately, but he doesn't, so it cannot be 8.
Could red's card say 7? Possible squares would be C1R4, C2R5, C3R6 (grey's square). It can't be C2R5, because that is 2 squares from both grey and black. That leaves C1R4 and C3R6. When they all say they don't know where it is, red knows that it can't be C3R6 (otherwise grey would have said he did know where it is).
That leaves C1R4.
Repeat this process assuming red's card says 6, 5, 4, 3, 2 or 1 and you will find that the number of possible squares increases as you move down that scale, which does not allow you to narrow it down to a single possible square when they declare themselves.
C1R4 is therefore the only possible place for the treasure.
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Post by bartlesby on Jan 13, 2018 23:29:15 GMT
Here is the answer. I'll name cells in the format C3R4, meaning column 3 (from the left), row 4 (from the top). What are the possible numbers that each card can say (i.e. how many squares can each squirrel move to)? R can say 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 G can say 0, 1, 2, 3, 4, 5, 6, 7, 8 B can say 0, 1, 2, 3, 4, 5, 6, 7 Clearly no card says 0 as they would know straightaway. Lets' focus on what red's card says. Key here is that he doesn't know immediately, but he does know when the other squirrels say they don't know. So we are looking for a situation where red's number allows him to immediately narrow it down to 1 free square and 1 or 2 occupied squares. When the squirrels say they don't know, the occupied squares are knocked out, leaving the 1 free square as the only possible option for red. Let's work through the possible options: Could red's card say 9? No, if it did he would know where it was immediately (C1R6), because he's the only one that can move 9 squares by the most direct route. Could red's card say 8? If it did, possible squares would be C1R5 and C2R6. But, C1R5 is 3 squares from both grey and black and everyone has a different number so that cannot be it. Which just leaves C2R6. I.e. if it 8, red would know immediately, but he doesn't, so it cannot be 8. Could red's card say 7? Possible squares would be C1R4, C2R5, C3R6 (grey's square). It can't be C2R5, because that is 2 squares from both grey and black. That leaves C1R4 and C3R6. When they all say they don't know where it is, red knows that it can't be C3R6 (otherwise grey would have said he did know where it is). That leaves C1R4. Repeat this process assuming red's card says 6, 5, 4, 3, 2 or 1 and you will find that the number of possible squares increases as you move down that scale, which does not allow you to narrow it down to a single possible square when they declare themselves. C1R4 is therefore the only possible place for the treasure. That's comprehensive but it's more intuitive to solve if you simply ask the right, simple questions. Here's how I'd sum my process of thinking up: Red is able to deduce for certain where the Golden Acorn is because Black and Grey don't immediately know the answer. Why would Red know that just based on their answers? What information have they provided to Red to come to this conclusion? They've provided the information that neither of them are holding 0 because otherwise they would be able to conclusively answer where it is. That information can only be useful to Red if he has a number that would land on one of their squares. Therefore, he has a 5 or a 7. Red knows he can only move in a direct path to the Golden Acorn. If he has a 5, that leaves five possible squares where the Golden Acorn could be. If he has a 7, that leaves two possible squares. Ruling out two possibilities is easier than ruling out five, so you start with the assumption he has a 7. That leaves C1R4 and C2R5. How did he figure out which one it was based on the information he had? Well, the squirrels cannot hold the same number, as stated by the rules. If the Golden Acorn was at C2R5, both Black and Grey would hold a 2 so it can also be ruled out-- leaving only C1R4 as the answer if Red has a 7. Since it's a riddle, it can only have one correct answer or doesn't have much point as a riddle, so you can be safely assured that narrowing it down to one possibility means you've found it. You could check to see what would happen if he had a 5 but you'd find them all to be inconclusive based on what Red could know. |
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Post by Flying Monkeys on Jan 13, 2018 23:58:12 GMT
They've provided the information that neither of them are holding 0 because otherwise they would be able to conclusively answer where it is. That information can only be useful to Red if he has a number that would land on one of their squares. Therefore, he has a 5 or a 7. That doesn't get you to the answer. So he has a 5. So what? It could be many squares if he has a 5. You need to think this through. |
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Post by bartlesby on Jan 14, 2018 0:09:25 GMT
They've provided the information that neither of them are holding 0 because otherwise they would be able to conclusively answer where it is. That information can only be useful to Red if he has a number that would land on one of their squares. Therefore, he has a 5 or a 7. That doesn't get you to the answer. So he has a 5. So what? It could be many squares if he has a 5. You need to think this through. It does get me the answer. That's how I answered it. The answer is based around Red being correct. He can only be correct once. I don't need to rule out the 5s if I've already found where he's correct by checking the 7s. |
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Post by Flying Monkeys on Jan 14, 2018 0:16:56 GMT
It does get me the answer. That's how I answered it. The answer is based around Red being correct. He can only be correct once. I don't need to rule out the 5s if I've found where he's correct. No. 5 gives him far too many possible squares for him to be able to narrow it down after the squirrels declare they don't know. 5 means it could be: C2R1 C1R2 C2R3 C3R4 C4R5 C5R6 From this range, you cannot deduce anything from a card showing 5, even when they say they don't know. |
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Post by bartlesby on Jan 14, 2018 0:23:37 GMT
It does get me the answer. That's how I answered it. The answer is based around Red being correct. He can only be correct once. I don't need to rule out the 5s if I've found where he's correct. No. 5 gives him far too many possible squares for him to be able to narrow it down after the squirrels declare they don't know. 5 means it could be: C2R1 C1R2 C2R3 C3R4 C4R5 C5R6 From this range, you cannot deduce anything from a card showing 5, even when they say they don't know. Yes, but that is why you don't try there at first and instead check out the 7s where there are only two possibilities. It's the more likely area for the answer to be in and even if it is not, it takes less time to rule out. It also happens to be where the answer is. Again, it's a riddle and they are crafted to only have one correct answer. All you need to do is find a correct one by its own rules and you've either solved it or shown it to be faulty. |
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Post by Flying Monkeys on Jan 14, 2018 0:33:50 GMT
Yes, but that is why you don't try there at first and instead check out the 7s where there are only two possibilities. It's the more likely area for the answer to be in and even if it is not, it takes less time to rule out. It also happens to be where the answer is. Again, it's a riddle and they are crafted to only have one correct answer. All you need to do is find a correct one by its own rules and you've either solved it or shown it to be faulty. Pfft. You don't try there at first, although you put that forward at first? Give it rest, I got this one, you didn't. |
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Post by bartlesby on Jan 14, 2018 0:37:52 GMT
Yes, but that is why you don't try there at first and instead check out the 7s where there are only two possibilities. It's the more likely area for the answer to be in and even if it is not, it takes less time to rule out. It also happens to be where the answer is. Again, it's a riddle and they are crafted to only have one correct answer. All you need to do is find a correct one by its own rules and you've either solved it or shown it to be faulty. Pfft. You don't try there at first, although you put that forward at first? Give it rest, I got this one, you didn't. I actually explained why I didn't try to solve 5s first. Maybe even twice now. Should we go for a third? |
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Post by Flying Monkeys on Jan 26, 2018 18:58:15 GMT
I actually explained why I didn't try to solve 5s first. Maybe even twice now. Should we go for a third? It's amazing how you got the answer after I posted it. |
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