A new mind twister
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You have 12 balls - one of which is either lighter or heavier than the others. Using a balance scale determine the odd ball and whether it is heavy or light in 3 weighings. This is much more difficult than it first appears. Have fun. Dave Huff 'tis a silly place!
- Put four balls in each scale to find a pile that contains normal balls. (If equal, then both weigthed piles, if not, the one not weigthted). 2) If eigth balls are found normal it is easy to find the odd one in two weighings. If not: Remove two ball from first scale, one from second scale and swap two of the remaining ones from scale to scale. Add one normal ball to have equal number of balls on each scale. Case 1: Scale is in balance - one of the three balls removed is the odd one. Case 2: Scale shifts - one of the two moved balls is odd. Case 3: Scale does not shift - one of the three unmoved balls are odd. 3.1) Place two of the odd balls from each scale on one of the scales. Balance with two normal balls on the other scale. Case 1: Scale in balance - The remaining ball is odd and it's status can be revealed from weighting 2). Case 2: The scale with the unknown balls are heavier/lighter - which one is odd can be determined from weighting 2) 3.2) Determine which is odd by comparing with a normal ball. 3.3) Do as 3.1) Is that the correct solution? /moliate
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Measure four against four. Possible results: 1) weigh the same - take three balls from a measured four and three of the remaining and weigh: if the same measure remaining ball is the one - measure it against known ball and you have whether it is heavy or light. if different you know whether it is heavy or light because you know the three balls already measured are the same. Measure one of the three unknows against another. If the same the last ball is the odd man. If not the same the heavier or lighter ball can be determined from previous step. This is the easy part. What to do if the 4 vs 4 do not weigh the same is where it gets hard. Dave Huff 'tis a silly place!
I already got that far:confused: Paresh Solanki There is no substitute for genuine lack of preparation.
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- Put four balls in each scale to find a pile that contains normal balls. (If equal, then both weigthed piles, if not, the one not weigthted). 2) If eigth balls are found normal it is easy to find the odd one in two weighings. If not: Remove two ball from first scale, one from second scale and swap two of the remaining ones from scale to scale. Add one normal ball to have equal number of balls on each scale. Case 1: Scale is in balance - one of the three balls removed is the odd one. Case 2: Scale shifts - one of the two moved balls is odd. Case 3: Scale does not shift - one of the three unmoved balls are odd. 3.1) Place two of the odd balls from each scale on one of the scales. Balance with two normal balls on the other scale. Case 1: Scale in balance - The remaining ball is odd and it's status can be revealed from weighting 2). Case 2: The scale with the unknown balls are heavier/lighter - which one is odd can be determined from weighting 2) 3.2) Determine which is odd by comparing with a normal ball. 3.3) Do as 3.1) Is that the correct solution? /moliate
moliate wrote: 2) If eigth balls are found normal it is easy to find the odd one in two weighings. If not: Remove two ball from first scale, one from second scale and swap two of the remaining ones from scale to scale. Add one normal ball to have equal number of balls on each scale. Case 1: Scale is in balance - one of the three balls removed is the odd one. At this point you have three balls and you still do not know whether they are heavier or lighter with only one weighing remaining. But its closer. Dave Huff 'tis a silly place!
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moliate wrote: 2) If eigth balls are found normal it is easy to find the odd one in two weighings. If not: Remove two ball from first scale, one from second scale and swap two of the remaining ones from scale to scale. Add one normal ball to have equal number of balls on each scale. Case 1: Scale is in balance - one of the three balls removed is the odd one. At this point you have three balls and you still do not know whether they are heavier or lighter with only one weighing remaining. But its closer. Dave Huff 'tis a silly place!
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Assuming you keep the two balls removed from the first scale separated from the one removed from the second one you could do it in one weighing... Or am I not thinking clearly here :confused: /moliate
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Narrowed down to max three balls in weighting 2) :~ - Unknown :) - Normal 1:~ 2:~ ----- 3:~ :) 1======= 2======= (scale 1 lighter) Take one :~ from each side: 2:~ 3:~ ----- :) :) 1======= 2======= Case 1: Scales in balance - 1:~ light Case 2: Scale 1 lighter - 2:~ light Case 3: Scale 2 lighter - 3:~ heavy Of course, replacing all light with heavy and the other way around will not change anything... The problem might be if the balls cannot be separated on the scale.. /moliate
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Narrowed down to max three balls in weighting 2) :~ - Unknown :) - Normal 1:~ 2:~ ----- 3:~ :) 1======= 2======= (scale 1 lighter) Take one :~ from each side: 2:~ 3:~ ----- :) :) 1======= 2======= Case 1: Scales in balance - 1:~ light Case 2: Scale 1 lighter - 2:~ light Case 3: Scale 2 lighter - 3:~ heavy Of course, replacing all light with heavy and the other way around will not change anything... The problem might be if the balls cannot be separated on the scale.. /moliate
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You have 12 balls - one of which is either lighter or heavier than the others. Using a balance scale determine the odd ball and whether it is heavy or light in 3 weighings. This is much more difficult than it first appears. Have fun. Dave Huff 'tis a silly place!
For convenience sake, name balls 1-12. * denotes normal balls. 1) Place balls 1-4 on one side of the scale, 5-8 on the other. If they weigh the same, 9-12 contains the odd ball (goto a.2). If they weigh different, 1-8 contain the odd ball (goto b.2). a.2) Place 9,10 on one scale, 11,1* on the other. If they weigh the same, 12 is the odd ball, weigh against a normal ball to determine heavy/light. If they weigh different, goto a.3 a.3) Place 9 on one, 10 on other. If they weigh same, 11 is the odd ball, and you know from a.2 whether it is heavy or light. If 9 is heavier, and 9,10 was heavier than 11,* then 9 is the heavy odd ball. If 9 is lighter, and 9,10 was heavier than 11,*, then 10 heavy odd ball. If 9 is heavier and 9,10 was lighter than 11,*, then 10 is the light odd ball. If 9 is lighter and 9,10 was lighter than 11,*, then 9 is the light odd ball. b.2) Place 1,5,6 on one side, 2,7,8 on the other. - If the scale is even, one of the following is odd: 3,4. Step (1) tells you if the odd ball is light or heavy, weigh them to figure out which is odd. - If the scale changes, the odd ball was moved, therefore, it is one of the following: 2,5,6. Goto c.3 - If the scale doesn't change, the odd ball wasn't moved, therefore, it is one of the following: 1,7,8. Goto d.3 c.3) The odd ball is 2,5,6. - If 1-4 was heavier than 5-8 (step 1), then 2 is heavy or 5 or 6 is light. Weigh 5,6. If they are even, 2 is the heavy odd ball. If 5 is light, 5 is the light odd ball. If 6 is light, 6 is the light odd ball. - If 1-4 was lighter than 5-8 (step 1), then 2 is light or 5 or 6 is heavy. Weigh 5,6. If they are even, 2 is the light odd ball. If 5 is heavy, 5 is the heavy odd ball. If 6 is heavy, 6 is the heavy odd ball. d.3) The odd ball is 1,7,8. Do something similar to c.3 to determine the answer.
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For convenience sake, name balls 1-12. * denotes normal balls. 1) Place balls 1-4 on one side of the scale, 5-8 on the other. If they weigh the same, 9-12 contains the odd ball (goto a.2). If they weigh different, 1-8 contain the odd ball (goto b.2). a.2) Place 9,10 on one scale, 11,1* on the other. If they weigh the same, 12 is the odd ball, weigh against a normal ball to determine heavy/light. If they weigh different, goto a.3 a.3) Place 9 on one, 10 on other. If they weigh same, 11 is the odd ball, and you know from a.2 whether it is heavy or light. If 9 is heavier, and 9,10 was heavier than 11,* then 9 is the heavy odd ball. If 9 is lighter, and 9,10 was heavier than 11,*, then 10 heavy odd ball. If 9 is heavier and 9,10 was lighter than 11,*, then 10 is the light odd ball. If 9 is lighter and 9,10 was lighter than 11,*, then 9 is the light odd ball. b.2) Place 1,5,6 on one side, 2,7,8 on the other. - If the scale is even, one of the following is odd: 3,4. Step (1) tells you if the odd ball is light or heavy, weigh them to figure out which is odd. - If the scale changes, the odd ball was moved, therefore, it is one of the following: 2,5,6. Goto c.3 - If the scale doesn't change, the odd ball wasn't moved, therefore, it is one of the following: 1,7,8. Goto d.3 c.3) The odd ball is 2,5,6. - If 1-4 was heavier than 5-8 (step 1), then 2 is heavy or 5 or 6 is light. Weigh 5,6. If they are even, 2 is the heavy odd ball. If 5 is light, 5 is the light odd ball. If 6 is light, 6 is the light odd ball. - If 1-4 was lighter than 5-8 (step 1), then 2 is light or 5 or 6 is heavy. Weigh 5,6. If they are even, 2 is the light odd ball. If 5 is heavy, 5 is the heavy odd ball. If 6 is heavy, 6 is the heavy odd ball. d.3) The odd ball is 1,7,8. Do something similar to c.3 to determine the answer.
You got it. One of the big tricks in figuring it out is to think of the balls not as known and unknown but as known, possibly lighter and possibly heavier. This allows you to cross reference and elimnate balls in the second weighing just as you did. Good job. Dave Huff 'tis a silly place!
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If your measuring six balls you have it wrong. Measuring six against six tells you exactly nothing. Dave Huff 'tis a silly place!
Actualy I measured 3 vs 3. If their equal, its not in that 6, its in the other 6. I would then compare 3 of the not equal set to 3 of the equal set to determine which 3 had the not equal ball. If I found the not equal 3 on this compare, I get the right ball by comparing 1 v1 from that 3 (as you know whether the ball is heavier or lighter), but it doesn't quite work for the other 3, you need an extra weighing. So my solution was flawed. Roger Allen Sonork 100.10016 If I had a quote, it would be a very good one.
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6 and 6 take lighter or heavier 6 3 and 3 take lighter or heavier 3 1 and 1 take lighter or heavier if they balance it's the ball thats left ;) This Sig For Rent
Corky6 and 6 That is the only first weighing that makes no sense whatsoever ... We were told one of the 12 balls has a different weight so we know before such a measurement what will happen - the scale will not balance and we still don't know any more than before. Steve T.