Nice puzzle You have 12 balls of same size and only one is different- is more heavy or light than other 11. You can use the scale 3times. Is it possible to tell which one?
Place 6 balls on each end of the scale. Determine the group which is heaviest. Devide the heavy group into two groups of three. Place each one end of the scale. Determine the group that is heaviest. With the heaviest group, place one ball on each end of the scale and keep the third in your hand. If the scales balance, the one in your hand is heavier. Otherwise, the scale will tip one way or another.
Good point - I'll put my thinking cap back on! Can you elaborate on the type of scale? I assumed a see-saw type balance. Are you stating it's more a kind of device that just shows a total weight in say a readout?
the scales looks like this - http://www.hdcentre.org/datastore/scales.jpeg (dont know how they're called in english)
Ok, I think this is pretty much it. Sure it's the right approach even if I've missed a combination or two... (1) Weigh 1,2,3,4 <> 5,6,7,8 If balances... (2) Weigh 1,9 <> 10,11 (note which way the side with 9 on goes) If balances... 12 is odd ball out (3) Weigh 1<>12 to see if 12 is heavier or lighter Else 9,10 or 11 are odd ones out (3) Weigh 10<>11 If balances Odd one out is ball 9 and we already know whether heavier or lighter from last step Else From step 2, we know if the odd ball is heavier or lighter, so depending on which way scale goes now, we know which is odd one out End if End if Else If 1,2,3,4 go up... We now know 9,10,11,12 can be eliminated (2) weigh 1,2,3<>4,5,6 If balances.. We know the odd ball is 7 or 8 and it's heavier (3) Weigh 7<>8 Else if 1,2,3 go up We know the odd ball is 4,5 or 6 and is heavier... (3) Weigh 4<>5 If balances, ball 6 is heavier Else lower ball is heavier Else if 1,2,3 go down We know the odd ball is 4,5 or 6 and is lighter... (3) Weigh 4<>5 If balances, ball 6 is lighter Else higher ball is lighter Endif Else if 1,2,3,4 go down... We now know 9,10,11,12 can be eliminated (2) weigh 1,2,3<>4,5,6 If balances.. We know the odd ball is 7 or 8 and it's lighter (3) Weigh 7<>8 Else if 1,2,3 go down We know the odd ball is 4,5 or 6 and is lighter... (3) Weigh 4<>5 If balances, ball 6 is lighter Else higher ball is lighter Else if 1,2,3 go up We know the odd ball is 4,5 or 6 and is heavier... (3) Weigh 4<>5 If balances, ball 6 is heavier Else lower ball is heavier Endif Endif Code (markup):
another one you have 9 balls one is heavir you are allowed 2 scales on a balance scale can you find the heavy one?