One of the Eight Coins is Counterfeit

You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?

Solution »

First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it's the counterfeit. If they have equal weight, the third coin is the counterfeit.

Ice Cube

A glass of water with a single ice cube sits on a table.

When the ice has completely melted, will the level of the water have increased, decreased or remain unchanged?

Solution »

Remain unchanged. When frozen, the ice cube displaces its weight.

Three Boxes of Black and White Marbles

Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels are wrong. You may reach into one of the boxes and pull out only one marble. Which box should you remove a marble from to determine the contents of all three boxes?

Solution »

The one labeled both. Since you know it's labeled incorrectly, it must have all black marbles or all white marbles. After you determine what it contains, you can identify the other two boxes by the process of elimination.