You have 8 balls. one of them is defective and weighs less than others. use a balabce to measure balls against

Question

each other. doing this twice. how do you find the defective one

Answer 1

easy.

weigh 3 + 3.

if =, weigh the other 2, and the lighter one wins.

if not =,  weigh 1 against 1 of the lighter set.

if =, the 3rd of the set is odd.

if not =, the lighter is lighter.

the harder version is when you have 12, and you don't know whether there is an odd ball, nor do you know whether it's heavier or lighter.  but the good news is that you get 3 weighings.

(1) to start, weigh 4+4

if not =, go to (BB)

if = you know you have 8 that are standard, and if there's an odd one, it's part of the other 4.

(2) weigh 3 of the other 4 against your standard.

(3) if = weigh the remaining against a standard.

(3) if not = you know whether it's heavier or lighter, weigh 1 against 1.

if = the 3rd is odd, and you know whether it's heavy or light.

if not = you already know whether the odd one is heavy or light, so you know which is odd.

(BB)  one of the 8 is odd.  for purposes of this description, we'll label the 4 on the light side L,L,L,L and the 4 on the heavy side, H,H,H,H.  the 4 that we didn't weigh we'll label S,S,S,S (standard).

now's the hard part.  you need to weigh 3 from the H group against 3 from L group.

and use the S group to compare.  but you don't have 6 in the S group.  So,

(2) weigh  L,L,H,H against H,L,S,S

if =, (3) weigh the remaining L,H against S,S and you can tell which is odd.

if not =, then is the 2nd hard part.

(CC)  if L,L,H,H is heavy, then EITHER H,H is heavy, OR the L in the H,L,S,S set is light.  SO,

(3) weigh one of the H's in the L,L,H,H set and the L in the H,L,S,S against two S balls.

  if they're = then the 3rd H is the odd one.

  if they're not = then, depending on whether they're heavy or light, you can identify the odd one.

if the (CC) goes the other way, then the logic is the same, only backward.

the trick to this is remembering to weigh 3 each, using both sides of the pan.