A merchant has 9 coins that look identical, but one is counterfeit and weighs slightly less than the rest. Using a two-pan balance scale without weights, what is the minimum number of weighings required to guarantee finding the counterfeit coin?
2
Divide the 9 coins into three groups of 3 (A, B, C). Weigh group A against group B. If they balance, the fake is in group C. If one is lighter, the fake is in that group. Take the 3 candidate coins and weigh any two against each other; if they balance, the unweighed one is fake. If one is lighter, it is the fake. Thus, 2 weighings suffice.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Medium. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
A courier must deliver four packages labeled W, X, Y, and Z. Package W must be delivered before X. Package Y must be delivered after Z, but before W. In what exact order are the packages delivered?
Two cars start driving toward each other from towns 300 miles apart. Car A travels at 60 mph, and Car B travels at 40 mph. At the exact same moment Car A starts, a remarkably fast falcon flies from Car A's roof toward Car B at 100 mph. When the falcon reaches Car B, it immediately turns around and flies back to Car A, repeating this until the cars crash. What total distance does the falcon fly?
Five house numbers on a street are consecutive even numbers. If the sum of all five house numbers is 170, what is the largest house number?
Three boxes are labeled 'Apples', 'Oranges', and 'Apples and Oranges'. All three labels are guaranteed to be incorrect. You are allowed to pull only one piece of fruit from the box labeled 'Apples and Oranges'. Which box must you draw from to determine the correct contents of all three boxes?
If you spell backwards the name of the month that is the shortest in length (by number of letters), what word do you get?
Three colored boxes are on a table: Red, Blue, and Green. One contains a coin, one contains a key, and one is completely empty. The label on the Red box says 'The coin is here.' The label on the Blue box says 'The Green box is empty.' The label on the Green box says 'The Red box contains the key.' If exactly one label is true, which box contains the coin?