Every night, Joe goes out to dinner with some friends from work, and then they go to a bar afterwards. Joe always pays the check at dinner with his credit card, and his friends pay him back with cash. He notices that when people are paying him back, they usually don't take into account how much their beer costs. So he announces a rule, "If you order beer at dinner, then buy me a drink when we go to the bar." His friends agree to this rule.

Of course, with the conversation going, Joe can't keep track of everything everyone orders at dinner. You want to see whether any of Joe's friends cheat on this rule.

The cards below represent four of Joe's friends. Each card represents one friend. One side of the card tells whether that person ordered beer at dinner and the other side tells whether that person bought Joe a drink at the bar.

Which of the following cards would you definitely need to turn over to see if any of these friends cheated on the rule:

"If you order beer at dinner,

then buy me a drink when we go to the bar."

Do not turn over any more cards than are absolutely necessary.

Fort Point army base is remote and isolated, and there's not even a lot to do in the nearby town. Occasionally, musicians or comedians will come and perform at the base. A band is coming to perform a show. Since he needs some ditches to be dug, the commanding officer has made a rule, "If you go to the concert, then you have to work a four-hour shift digging ditches."

You want to see whether any of the soldiers have broken the rule.

The cards below represent four soldiers. Each card represents one soldier. One side of the card tells whether that soldier went to the concert and the other side tells whether that soldier did a shift digging ditches.

Which of the following cards would you definitely need to turn over to see if any of these soldiers have broken the rule:

"If you go to the concert,

then you have to work a four-hour shift digging ditches."

Do not turn over any more cards than are absolutely necessary.

At Williamson's paint factory, the company has a community fund, made up of donations by factory workers, that it uses to do things for factory workers when they are in need. Workers sometimes do favors for each other, like covering a work shift if a person has a doctor's appointment or if their kid is sick. The company allows this, but they have a rule, "If you get someone else to cover a work shift for you, then make a donation to the community fund."

You want to see whether any factory workers ever break this rule.

The cards below represent four factory workers. Each card represents one worker. One side of the card tells whether that worker has had someone else cover a work shift for them and the other side tells whether that worker made a donation to the community fund.

Which of the following cards would you definitely need to turn over to see if any of these workers have broken the rule:

"If you get someone else to cover a work shift for you, then make a donation to the community fund."

Do not turn over any more cards than are absolutely necessary.

Lots of kids go to summer camp during their summer vacation from school, and spend time hiking, swimming, boating and making arts and crafts. At Fallen Leaf Lake Camp, the kids' favorite activity is canoeing on the lake. The camp counselors have a rule, "If you go canoeing on the lake, then you must have a clean bunk house."

You want to see whether any of the kids ever break this rule.

The cards below represent four kids at Fallen Leaf Lake Camp. Each card represents one kid. One side of the card tells whether that kid went canoeing on a particular day and the other side tells whether that kid had a clean bunk house that day.

Which of the following cards would you definitely need to turn over to see if any of these kids broke the rule:

"If you go canoeing on the lake, then you must have a clean bunk house."

Do not turn over any more cards than are absolutely necessary.

Alabama Getaway is a big family resort hotel at the beach in Mobile, Alabama that has its own miniature golf course. The hotel has a rule, "If you play on our miniature golf course, then you have to be staying at Alabama Getaway."

You want to see whether anyone in Mobile ever breaks this rule.

The cards below represent people in Mobile. Each card represents one person. One side of the card tells whether that person is playing on the hotel's miniature golf course and the other side tells whether that person is staying at Alabama Getaway.

Which of the following cards would you definitely need to turn over to see if any of these people are breaking the rule:

"If you play on our miniature golf course,

then you have to be staying at Alabama Getaway."

Do not turn over any more cards than are absolutely necessary.

The County Council of Auburn County, Minnesota has a law about toxic waste disposal in their county. They say to companies that want to dispose of toxic waste there, "If you put a toxic waste dump in our county, then give jobs to people from this county."

You want to see whether any companies ever break this law.

The cards below represent different companies. Each card represents one company. One side of the card tells whether that company put a toxic waste dump in Auburn County and the other side tells whether that company gave jobs to people from Auburn County.

Which of the following cards would you definitely need to turn over to see if any of these companies broke the law:

"If you put a toxic waste dump in our county,

then you must give jobs to people from this county."

Do not turn over any more cards than are absolutely necessary.

Rolling Hills, California is a town with very wealthy people. Everyone there wants to own a horse, but the City Council of Rolling Hills knows that horses like to have a lot of space to move around in. They think that anyone who doesn't understand this probably shouldn't be a horse owner, so they have a law, "If you own a horse, then you have to have a pasture that is at least 3 acres."

You want to see whether anyone in Rolling Hills ever breaks this law.

The cards below represent four people who live in Rolling Hills. Each card represents one person. One side of the card tells whether that person owns a horse and the other side tells whether that person has a pasture that is at least 3 acres.

Which of the following cards would you definitely need to turn over to see if any of these people have broken the law:

"If you own a horse,

then you have to have a pasture that is at least 3 acres."

Do not turn over any more cards than are absolutely necessary.

The O'Brien's want their children to keep their rooms clean, so they made a rule: "If you watch TV, your room has to be clean."

You would like to find out whether any of the O'Brien's kids ever cheat on this rule.

The cards below have information on what four of their kids did. Each card represents one kid. One side of the card tells whether that kid is watching TV and the other side tells whether that kid's room is clean. Which of the following cards would you definitely need to turn over to see if any of the O'Brien kids cheated on the rule:

"If you watch TV, your room has to be clean."

Do not turn over any more cards than are absolutely necessary.

At the Corner Comedy club, to make money, they have the rule, "If you watch the comedy show, then you have to buy at least two drinks."

Imagine that you work for the comedy club, and you want to check whether people ever cheat on this rule.

The cards below represent four people. Each card represents one person. One side of the card tells whether the person watched the comedy show and the other side tells whether the person bought drinks.

Which of the following cards would you definitely need to turn over to see if any of these people have cheated on the rule:

"If you watch the comedy show, then you have to buy at least two drinks."

Do not turn over any more cards than are absolutely necessary.

In the county school system, teachers are allowed to take a vacation during the summer. They are also allowed to take vacations earlier than the summer, but if so, there is a rule: "If you take your vacation early, then you must work extra hours."

Imagine you work for the school district, and you want to check whether any teachers ever cheat on this rule.

The cards below have information about four teachers. Each card represents one teacher. One side of the card tells whether that teacher took his or her vacation early, and the other side tells whether that teacher worked extra hours. Which of the following cards would you definitely need to turn over to see if any of these teachers have cheated on the rule:

"If you take your vacation early, then you must work extra hours."

Do not turn over any more cards than are absolutely necessary.

Joe is a college student who owns a motorcycle, which he sometimes lets his friends borrow. He likes to keep his motorcycle looking shiny and new, so he gives his friends the following deal: "If you borrow my motorcycle, then wash it."

You would like to find out whether any of Joe's friends cheat on this rule. The cards below have information on what four of Joe's friends did on four different days.

Each card represents one friend on a different day. One side of the card tells whether that friend borrowed Joe's motorcycle and the other side tells whether that friend washed the motorcycle. Which of the following cards would you definitely need to turn over to see if any of Joe's friends cheated on the rule:

"If you borrow my motorcycle, then wash it."

Do not turn over any more cards than are absolutely necessary.

Some stores don't like to take credit cards unless they are sure that the card belongs to you. Many stores have the rule, "If you pay with a credit card, then you must have a picture ID." Some people try to cheat on this rule, and some store clerks let them get away with it.

Imagine that you are a store manager, and you want to check whether people ever cheat on this rule.

The cards below represent four different customers. Each card represents one customer. One side of the card tells whether the person paid with a credit card and the other side tells whether the person had a picture ID.

Which of the following cards would you definitely need to turn over to see if any of these people have cheated on the rule:

"If you pay with a credit card, then you must have a picture ID."

Do not turn over any more cards than are absolutely necessary.

In many countries, there are certain rules around elections. One rule is: "If you vote in an election, then you must be a citizen."

Imagine you are an election official and you want to find out whether anyone ever cheats on this rule.

The cards below have information about four people. Each card represents one person. One side of the card tells whether that person voted in the election and the other side tells whether that person is a citizen. Which of the following cards would you definitely need to turn over to check whether any of these people cheated on the rule:

"If you vote in an election, then you must be a citizen."

Do not turn over any more cards than are absolutely necessary.

In the county school system, teachers are allowed to take a vacation during the summer. They are also allowed to take vacations earlier than the summer, but if so, there is a rule: "If you take your vacation early, then you must work extra hours."

Imagine you work for the school district, and you want to check whether any teachers ever cheat on this rule.

The cards below have information about four teachers. Each card represents one teacher. One side of the card tells whether that teacher took his or her vacation early, and the other side tells whether that teacher worked extra hours. Which of the following cards would you definitely need to turn over to see if any of these teachers have cheated on the rule:

"If you take your vacation early, then you must work extra hours."

Do not turn over any more cards than are absolutely necessary.

Being a star athlete in college is a big honor, but college students have to abide by the rule, "If you are on a sports team, then you have to have good grades." Some players try to cheat on this rule, and some coaches let them get away with it.

Imagine that you work for a college, and you want to check whether people ever cheat on this rule.

The cards below represent four different students. Each card represents one student. One side of the card tells whether the student is on a sports team and the other side tells whether that student has good grades.

Which of the following cards would you definitely need to turn over to see if any of these students have cheated on the rule:

"If you are on a sports team, then you have to have good grades."

Do not turn over any more cards than are absolutely necessary.