Suppose you have 5 coins, one of which is counterfeit (either heavier or lighter than the other four). You use a pan balance scale to ﬁnd the bad coin and determine whether it is heavier or lighter.
(a) Prove that 2 weighings are not enough to guarantee that you ﬁnd the bad coin and determine whether it is heavier or lighter.
(b) Draw a decision tree for weighing the coins to determine the bad coin (and whether it is heavier or lighter) in the minimum number of weighings.

Question

Suppose you have 5 coins, one of which is counterfeit (either heavier or lighter than the other four). You use a pan balance scale to ﬁnd the bad coin and determine whether it is heavier or lighter. 
(a) Prove that 2 weighings are not enough to guarantee that you ﬁnd the bad coin and determine whether it is heavier or lighter. 
(b) Draw a decision tree for weighing the coins to determine the bad coin (and whether it is heavier or lighter) in the minimum number of weighings.

Quizplus · Accepted Answer

The Answer of Suppose you have 5 coins, one of which is counterfeit (either heavier or lighter than the other four). You use a pan balance scale to ﬁnd the bad coin and determine whether it is heavier or lighter. 
(a) Prove that 2 weighings are not enough to guarantee that you ﬁnd the bad coin and determine whether it is heavier or lighter. 
(b) Draw a decision tree for weighing the coins to determine the bad coin (and whether it is heavier or lighter) in the minimum number of weighings.

Suppose You Have 5 Coins, One of Which Is Counterfeit