Question

In a collection of 400 coins, one is counterfeit and weighs either more or less than the genuine coins. Find a good lower bound on the number of balance scale weighings needed to identify the fake coin and determine whether it is too heavy or too light. Assume the balance scale has three states: tilted left, tilted right, or balanced.

At least _____ weighings are needed?

Answer 1

ANSWER

0 Answel Step! We have a collection of 400 coins in which one is counterfeit and weights either more on less than the genuine coins. Now the balance scale is an opeeation with three possible outcomes. It could tilted left, tilted right , or balance evently Also, since of the 400 coins are to be checked for weighing either less or more, Hence there are 800 possible outcomes. Steps: We Hence, by theorem 5.1 can say that a lower bound on the numbee of balance scale weighings needed to identify the fake coin is (1083 (200)- 7 At least 1 weighing we needed