You have n balls of uniform appearance, and a scale : the scale has one arm, sup

Question

You have n balls of uniform appearance, and a scale : the scale has one arm, supported in the center, with a bowl on each end; you place balls in each bowl, and thescale will either go -up left (U), or -down left (D), or stay- equal (E).

To show that something can be done, you simply give the procedure and argue why it will work in all cases. To show something can NOT be done is harder... you have to either exhaustively survey all possible procedures (which will often be impossible in practice, since there are too many possible procedures...) – or find a feature of the problem that allows you to argue that it is logically impossible to do it.In our case you should exploit the idea that a “weighing” is like a question with a three-way answer (U,D, or E) instead of the usual two – way answer (“yes” or “no”, “true” or “false”, etc.). So, every time you do a weighing, you essentially are reducing the initial uncertainty about what is the case by cutting the “space of all possibilities” into three parts. This idea also gives you a good “heuristic” about what procedures might give the desired result: you will maximize the “information gained” from a weighing by making sure that it will cut the space of possibilities into (approximately) equal parts...!

You have four balls, and you know that exactly one of the balls has a deviant weight (i.e. it is lighter (L) or heavier (H) than the rest of the balls, which are standard, or normal (N).) Can you locate the deviant ball, AND determine if it is light or heavy, in only two weighings?If yes, describe the procedure to follow, and give reasons why your procedure will work in all cases. If no, give a reason why it can not be done.

Explanation / Answer

Yes coming to the 4 balls case

take 2 balls and weigh it and then there will be 2 cases

1. suppose if both weigh same then now take the remaining two balls and weigh them and now in these 2 you can find the different one

2. suppose if they weigh different then Then pick up another ball from the rest two and replace it with any one ball in the balance. Now again there are further 2 possibilities :

1.If the weights are same : Then the ball you just removed from the balance is the odd ball.

2.If the weights are different : Then the ball which was not replaced and is still in the balance is the odd one out.

by this in 2 steps you can find out the heavier or lighter one

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