Jim and Wanda both have some apples. If Jim gives Wanda an apple, they will both have the same number of apples. However, if Wanda gives Jim an apple, Jim will have twice as many as Wanda. How many apples do Jim and Wanda each have?
Suppose you have twelve eggs and a balance scale. All of the eggs are identical except for one whose only difference is its weight. Using the scale only three times, determine which egg is the odd egg out and whether it is heavier or lighter than the other eggs.
Weigh four against four. If they’re equal, weigh three of them against three you haven’t weighed. If they balance too, weigh the last remaining egg against any of the others to see if it is lighter or heavier. If the three suspects are heavier, weigh one of them against another and the one that goes down is it. If they balance the remaining suspect is heavy. Use the same process if they’re lighter. If the initial four vs four don’t balance, weigh two heavy eggs and a light egg against one heavy egg, one light one and a known normal egg. If they balance weigh the remaining two light eggs against each other. If they balance the unweighed heavy egg is the odd one out. If the side with two heavy eggs goes down weigh them against each other. If they balance it is the light egg on the other side. If the other side goes down it is either because of one heavy egg on that side or because the one light egg on the other side is lighter than the rest. Weigh one of them against a known normal egg to determine which is true.
King Ferdinand has no immediate living relatives and decides to hold a contest to find a worthy successor when he dies. He gives a seed to every contestant and explains that the person with the healthiest and most beautiful plant will win the throne.
When the final day of the contest arrives, the king finds hundreds of plants of all shapes and sizes. However, he ignores them and awards the throne to a girl holding a pot with only moist dirt.
King Ferdinand was a kind and trusting man and wanted to be sure he found an honest heir. He gave small pebbles to all the contestants, claiming they were seeds. Therefore, any contestant with a plant had switched their “seed” in order to win. Everyone but the girl had been dishonest.
