How many trials at least ...

somashekar

Staff member
Super Moderator
#1
9 balls of same shape, size and color.
8 balls weigh exact 997 gms each and 1 weighs exact 1000 gms.
You have a beam balance.
What minimum times the balance has to be used to pick the 1000 gms ball from the 9 balls... and how ?
 

Jim Wynne

Super Moderator
#2
Minimum is one trial, but it doesn't take more than two.

First trial: put three balls on each side of the scale. If the scale balances, you know that the ball is one of the three not on the scale.

Second trial: Put one ball of the three on each side of the scale. If it balances, you know that the lightest ball is the one not on the scale. If it doesn't balance, you also know which is the lightest.

In the first trial, if the scale doesn't balance, you've narrowed it down to three balls, and the second trial proceeds as above.

Note that the possibility of solving in one trial requires luck; you put four balls on each side of the scale and if it balances, you know that the one not on the scale is the light one.

ETA: Wherever I said "light" or "lightest" above, I meant "heavy" or "heaviest."
 
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