u should get 1000 points if u can solve this riddle?

Question

U are given 12 balls and a scale . U must find the odd ball i.e. one ball is either lighter or heavier than the other 11 . U don't get weights .U place balls on both sides of scale and observe whether the one side goes up or down U get 3 chances to weigh and then u must tell which ball it is and wether it is lighter or heavier than the other11 . U will soon see that it is not possible BUT IT IS.

Answer 1

Number the balls 1 to 12. Weigh 1, 2, 3, and 4 against 5, 6, 7, and 8.
If (1, 2, 3, 4) and (5, 6, 7, 8) balance:
Weigh 9 and 10 against 11 and 8 (we know 8 is not the odd ball).
If (9, 10) and (11, 8) balance: then 12 is the odd one.

Weigh 12 against any other to find out if it is heavy or light.

If (9, 10) and (11, 8) do not balance: suppose 11 and 8 are heavier,
than 9 and 10; then either 11 is heavy, or 9 is light, or 10 is light.

Weigh 9 against 10; if they balance, 11 is heavy; if they do not,
the lighter of 9 and 10 is the odd ball.

(Similar argument if 11 and 8 are lighter than 9 and 10).

If (1, 2, 3, 4) and (5, 6, 7, 8) do not balance:
Suppose 5, 6, 7, and 8 are heavier than 1, 2, 3, & 4. Then: one of
(1, 2, 3, or 4) is light, or else one of (5, 6, 7, or 8) is heavy.
Weigh 1, 2, and 5 against 3, 6, and 9.
If they balance: then either 7 is heavy, or 8 is heavy, or 4 is light.
Weigh 7 against 8; if they balance, 4 is the odd ball, otherwise the
heavier of 7 and 8 is the odd ball.

If (1, 2, 5) and (3, 6, 9) do not balance: suppose 1, 2, and 5 are lighter
than 3, 6, and 9; then either 6 is heavy, or 1 is light, or 2 is light.
Weigh 1 against 2 to find out which one of the three choices is true.
Otherwise, suppose 1, 2, and 5 are heavier than 3, 6, and 9; then either 3
is light, or 5 is heavy.

Weigh 3 against (say) 2 to find out which of the two choices is true.

(Similar argument if 1, 2, and 5 are lighter than 3, 6, and 9).

Answer 2

This is just for all the people that think you can measure 6 balls on one side and six on the other cuz two people already answered it correctly. The problem states that you don't know if the odd ball is lighter or heavier, so measuring 6 of them wouldn't prove anything cuz then you wouldn't know which of the two sets contains either a lighter ball or a heavier ball making that weigh in useless. You do have to split them into three groups of four, but their are so many different possibilities based on the first and second weigh ins which is what makes it so confusing and difficult.

Answer 3

First, label each ball: [A B C D E F G H I J K L]

Turn #1: Place on the balance: [A B C D] and [E F G H]
There are two possible T1 outcomes: [A B C D] is level, or it is not

1) If T1 was level, we know that the the odd ball is one of [I J K L]
We also know that [A B C D E F G H] are all standard weight

Turn #2a: Place on the balance: [I J] and [K A] (where [A] is standard)
There are three possible T2a outcomes: [I J] is level, heavier, or lighter

a) If T2a was level, we know that the odd ball is [L]

Turn #3a: Place on the balance: [L] and [A]
Observe if [L] is heavier or lighter

b) If T2a showed [I J] heavier, we know one of [I J] is heavier, OR [K] is lighter

Turn #3b: Place on the balance: [I] and [J]
If level, then [K] is lighter
Otherwise observe which is the heavy ball: [I] or [J]

c) If T2a showed [I J] lighter, we know either [I] or [J] is lighter, OR [K] is heavier

Turn #3c: Place on the balance: [I] and [J]
If level, then [K] is heavier
Otherwise observe which is the light ball: [I] or [J]

2) If T1 was not level, relabel the heavier side [A' B' C' D'] and the lighter side [E' F' G' H']
We know one of [A' B' C' D'] is heavier, OR one of [E' F' G' H'] is lighter
We also know that [I J K L] are all standard weight

Turn #2b: Place on the balance: [A' B' I] and [C' D' E']
There are three possible T2b outcomes: [A' B' I] is level, heavier, or lighter

a) If T2b was level, we know that one of [F' G' H'] is lighter

Turn #3d: Place on the balance: [F'] and [G']
If level, then [H'] is lighter
Otherwise observe which is the lighter ball: [F'] or [G']

b) If T2b showed [A' B' I] heavier, we know either [A'] or [B'] is heavier, OR [E'] is lighter

Turn #3e: Place on the balance: [A'] and [B']
If level, then [E'] is lighter
Otherwise observe which is the heavier ball: [A'] or [B']

c) If T2b showed [A' B' I] lighter, we know either [C'] or [D'] is heavier

Turn #3f: Place on the balance: [C'] and [D']
Observe which is the heavier ball: [C'] or [D']

Answer 4

Ok here goes: split the balls into 2 sixes and weigh. Then split into 2 three"s the lighter or heavier. Then put one ball each on the scales and keep hold of one. The scales will tell you which is different and if they are the same then the ball in your hand is the odd one.

Answer 5

put 6 balls on one side and 6 on the other of the measuring scale. the one side with the heavier ball will be obviously heavy! so discard the 6 balls on the other side

now divide them into 3 each. measue again and keep the heavier side and discard 3 more balls the same way u discarded the first time

now take 2 balls out of these 3 and measure if one ball is heavy the measuring scale will lean that side so u'd know which one is heaviest, if both sides are equal u wud know the third one was the heaviest!!


^_~ gimme my 1000pts now!

Answer 6

ok first you put 6 on one side then 6 on the other. then with the heavier side u take it then u put 3 on both sides then with the heavier side you put 2 on then if theyre equal then the one that u didnt weigh is the odd ball then if one if heavier than the heavier ball is heavier.

Answer 7

Put 6 on each side.
The side that dips divide in two.
Now put your 3 balls on both sides.
One side will dip.
Discard the ones from the side that was lighter.
One of the 3 remaining is the ball.
Weigh 2 against each other. If one dips that is the odd ball, if neither dips you have the odd ball off the scale.

Answer 8

weigh six on each side the first time.. Take the heavier six and split them in three and weigh those two groups and find the heavier group.. Then take two of the three balls left and put them on the scale (thats your third chance to weigh)-- if they weigh the same, then the one in your hands is the heaviest.. if one of the two on the scale is heavier, then that one is the heaviest! EASY!!! =]

Answer 9

pick up ball 1. remember how heavy it feels. then go through the other balls while you load them on the scale until you find one thats heavier or lighter. If they don't, then ball1 is it.

Answer 10

Weigh 6 against the other six
The heaviest six get discarded

Weigh three against three (of the 6 left)
The heaviest get discarded

You then have three left
weigh one against one

If theyre even then the one you're left with is the ball
If one is lighter then thats the one