Using a balance scale, what's the least number of times you need to use it in order to find the "false" coin?
Topic: Case ss number
June 25, 2019 / By Colman Question:
You're given nine coins that look identical but aren't. Eight of them are made of gold. the ninth one is made of a diffrent, lighter metal. Using a balance scale, what's the least number of times you need to use it in order to find the "false" coin?
Best Answers: Using a balance scale, what's the least number of times you need to use it in order to find the "false" coin?
Areli | 5 days ago
If you are lucky, the least number of times would be ONE (if by chance you select the non-gold coin to compare with a gold coin, you will know immediately which one is lighter). I think your question wants to know the MAXIMUM number of times you would need to use the scale; in that case it would be FOUR (if by chance the first four pairs of coins you pick up and measure happen to be the 8 gold coins, which would obviously balance out) - which means the leftover coin would HAVE to be the non-gold one, no weighing necessary :)
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Originally Answered: How do you find this poem? scale of 1 -10?
The only good thing about this is the analogy, and how it starts the exact same way it ended. The poetic structure and word choice is just awkward and elementary to me. I would suggest starting over with the same idea.
Weigh four on one side of scale, four on the other side.
If the two sides balance equally, then the non-weighed coin is the lighter coin.
If the two sides are unbalanced, then,
WEIGH #2: divide the four coins on the lighter side into two groups of two and put on each side of the scale.(removing the four coins from the initial heavy side of course) Again, one side should be lighter. Take the two coins on the lighter side and
WEIGH #3: place each of the two coins on each side of the scale.(removing the two from the heavy side of course) The one that is lighter is of course the lighter coin.
So, if you get lucky then one use of scale might do it. But, most likely you will need to use the scale three times to get the answer.
You have a 1/9 chance of picking the right coin. and one use of scale will be necessary. (1/9 x 1 = 1/9)
You have an 8/9 chance of not picking the right coin. and three uses of scale will be necessary (8/9 x 3 = 24/9)
so on average you will require 25/9 (or 2.7) uses of scale if you did this an infinite number of times.
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First put 4 on 1 side and four o the other
if they balance then the 1 left out is false coin
2. if one side is lighter
then take the lighter side and put 2 and 2
3. Take 2 coins on the lighter side and weigh 1 on 1
lighter coin is the false coin
Thus max weighing required is 3.
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The least number of times is one.
Place one coin on each side of the balance scale. If the scale tilts to the left the coin on the right side is the false coin. Likewise, if it tilts to the right, the left coin is false.
Even it the scale balances, you would keep one coin on the left and alternately add a coin to the right until the scale went out of balance.
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