Question

1.13 (Counterfeit Coin Problem) We are given six coins, one of which is counterfeit and is known to have different weight than the rest. Construct a strategy to find the counterfeit coin using a two-pan scale in a minimum average number of tries. Hint: There are two initial decisions that make sense: (1) test two of the coins against two others, and (2) test one of the coins against one other.

Answer 1

Given that : there are six coins, among one is couterfeit weight than the rest

strategy:

divide six coins into 3 parts

2 coins, 2 coins, 2 coins

now :test any of two coins agains another two coins (remember that there are other two coins also which are not weighing)

//here counter feit coin may present in these four or may be not

lets see both the case

case1: //if present

then one of them will weigh more than other pair

so select that pair which is heavier

and test those two coins one against another, we will find the heavier one

case2: //if not present

then counterfeit coin must be present in other pair which is not weighing

so, take that pair

and test those two coins one against another, we will find the heavier one

//so in all cases

inorder to find counterfeit coin, in this strategy

we need 2 tries

//PLS give a thumbs up if you find this helpful, its helps alot, thanks