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Numbered Foreheads


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#1 ThunderCloud

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Posted 03 February 2013 - 12:44 AM

Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?


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#2 bushindo

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Posted 03 February 2013 - 01:46 AM

Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

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#3 googon97

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Posted 03 February 2013 - 02:39 AM

Spoiler for quick logic


Edited by googon97, 03 February 2013 - 02:44 AM.

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#4 ThunderCloud

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Posted 03 February 2013 - 03:01 AM

 


Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

Spoiler for

 

Spoiler for

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#5 ThunderCloud

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Posted 03 February 2013 - 03:20 AM

Spoiler for quick logic

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#6 bushindo

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Posted 03 February 2013 - 03:38 AM

 


Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

Spoiler for

 

Spoiler for

 

If the two logicians are required to give up if they figure they would never know it, then the game would go as follows

Spoiler for

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#7 ThunderCloud

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Posted 03 February 2013 - 03:51 AM

 

 


Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

Spoiler for

 

Spoiler for

 

If the two logicians are required to give up if they figure they would never know it, then the game would go as follows

Spoiler for
Spoiler for

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#8 bushindo

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Posted 03 February 2013 - 04:18 AM

 

 

 


Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

Spoiler for

 

Spoiler for

 

If the two logicians are required to give up if they figure they would never know it, then the game would go as follows

Spoiler for
Spoiler for

 

I see what you're saying

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#9 ThunderCloud

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Posted 03 February 2013 - 04:34 AM

 

 

 

 


Three logicians had stickers placed on their foreheads so that none could see their own sticker but each could see one another's. They were told that each sticker has a single positive integer written on it (i.e. 1, 2, 3, ...), and that the sum of the integers on all three stickers is either 8 or 9. They were then asked, in turn, to identify the number on their own sticker. Upon being asked, each logician would name their number if they were sure that they knew it, give up if they were sure that they would never know it, or otherwise 'pass' so that the question would be posed to the next person. The question was repeated, again in turn, until each of the three logicians had either named their number or given up. All three stickers had the same number written on them. Who among the three logicians was able to deduce his number?

 

Answer

Spoiler for

 

Spoiler for

 

If the two logicians are required to give up if they figure they would never know it, then the game would go as follows

Spoiler for
Spoiler for

 

I see what you're saying

Spoiler for
Spoiler for

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#10 bushindo

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Posted 03 February 2013 - 07:19 AM

Spoiler for

 

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