Math

posted by .

Steven has 9 gold coins that are identical in appearance. However, one coin is counterfeit an weighs slightly less that the others. Using a balance scale, how can he find the counterfeit coin in just two weighings?

  • Math -

    Split the coins into three groups, A, B and C consisting of 3 coins in each group.

    Weigh: A--B
    1. If A=B, the the counterfeit is in group C
    Weigh any two coins in group C and figure out the rest.

    2. If A≠B, then the counterfeit is in the lighter group.
    Weigh any two coins in the lighter group and figure out the rest.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    THE MIDAS TOUCH King Midas was a very wealthy and powerful king who ruled over 10 states. Each year each of the states would have to send him, as taxes, a bag fi lled with 100 gold coins. Each gold coin would have to weigh exactly …
  2. college

    A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel copy. The dealer heated the coin, which weighed 14.0 g to 100°C in boiling water and then dropped the hot coin into 29.5 g of water at T = …
  3. chemistry

    A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel copy. The dealer heated the coin, which weighed 14.0 g to 100°C in boiling water and then dropped the hot coin into 29.5 g of water at T = …
  4. math

    In a group of 9 coins, one is fake and weighs slightly more. What is the fewest number of times you need to use a pan balance to find the counterfeit coins?
  5. IWU

    You are considering buying 27 silver coins that look alike, but you have been told that one of the coins is a lightweight counterfeit. Find the least number of weighings on a balance scale that you can use to be certain you have found …
  6. math

    1. Finding the Counterfeit Coin. You have 5 coins. You know that one of them is counterfeit and weighs less than the others. Suppose also that you have a balance scale. Is there a strategy for finding the counterfeit coin using the …
  7. Chemistry

    A coin dealer, offered a rare silver coin, suspected that it might be a counterfeit nickel copy. The dealer heated the coin, which weighed 14.0 g to 100°C in boiling water and then dropped the hot coin into 27.5 g of water at T = …
  8. Math

    In a group of 9 coins, one is fake and weighs slightly less. What is the fewest number of times you need to use a pan balance to find the counterfeit coins?
  9. statistics and probabilities

    You have two coins that look identical, but one of them is fair and the other is weighted. The weighted coin has a 3/4 chance of flipping heads and a 1/4 chance of flipping tails. Unfortunately, you've forgotten which coin is which! …
  10. statistics

    You have two coins that look identical, but one of them is fair and the other is weighted. The weighted coin has a 3/4 chance of flipping heads and a 1/4 chance of flipping tails. Unfortunately, you've forgotten which coin is which! …

More Similar Questions