Mind Illusions

These puzzles are not easy. Many of the answers just feel wrong. Puzzles with counterintuitive solutions are traditionally called “veridical paradoxes”, but I like to call them “mind illusions.”
What are Mind Illusions?

We’re all familiar with optical illusions. These are images that demonstrate that our eyes can fool us. Mind illusions are puzzles or brainteasers that demonstrate that our minds can fool us.

Our intuition is excellent at making fast judgments, but not always for making correct ones. When we make judgments quickly, we can get things wrong. When we have the luxury of time, it is worth thinking about things slowly and carefully before making decisions or drawing conclusions.

Just like we might need a ruler or some other tool to make correct judgments when faced with an optical illusion, we need slow, careful thought to make correct judgments when faced with mind illusions.

These puzzles are ranked in order of difficulty (from easiest in yellow to hardest in blue), but even adults frequently get even the easiest ones wrong.

Highly intelligent children tend to have friends who are less intelligent than they are. Why? You post an online survey asking, 'Do you like surveys?' 100 peoople fill out the survey. 95 of them answer 'Yes'. You conclude, 'Most people like surveys!' Why is this a mistake? A ball and a bat together cost $1.10. How much does the ball cost? You are responsible for choosing where to put shields on new spaceships. You study the patterns of damage on spaceships that came back from battle. On which parts is it most important to put the shields? If a card has a vowel on one side, then it has an even number on the other side. Which cards must be flipped to decide if this statement is true for these four cards? You wrap a band around the equator so that it touches the ground at all places. Then you add 10 meters to the length of the band. How far will it rise above the ground? You are standing at the South Pole. You walk 1 kilometer north. You stop and turn 90 degrees. Will you reach the South Pole again? Will you reach the point where you turned? You have 100 kg of potatoes that are 99% water by weight. They dehydrate, and now they are 98% water by weight. How much do they weigh now? You are on a game show. You have to choose between one of three doors. Behind one of them is a car; behind the other two, goats. You will win whatever is behind the door you choose.