Double 6 Puzzle

Why the difference?

In puzzle 1, the die under the table is a complete mystery, so it still has its usual chances: one chance in six of also being a 6. Seeing a 6 on a particular die doesn’t change the second die’s ordinary roll chances.

In puzzle 2, all you know is that somewhere in the pair at least one 6 has appeared. If you look at all 36 outcomes of a roll of 2 dice, you see there are 11 different outcomes in which there is at least one 6. Only one of those 11 outcomes is the double six.

More Puzzles

You can buy a printable version of these puzzles.

Can you solve the baseball puzzle? A ball and a bat together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

There are three crates, one with apples, one with oranges and one with both apples and oranges mixed. Each crate is closed. They were labeled with one of three labels: “Apples”, “Oranges”, or “Apples and Oranges”, but a prankster came and switched all the labels.

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?

What is the shortest path for the spider to reach the fly?

In an alien species, every family keeps having children, one at a time, until they have one female child.

You have a stack of eight shuffled, face-down cards numbered 1 through 8. You turn over cards one at a time and get $100 for each card you turn over.

In a group of four people, what are the chances that two or more of them were born in the same month?

Even though driving at a higher speed increases the likelihood of a road collision, most collisions occur at moderate speeds. Why?

There are two bags - one with two gold coins, and the other with a gold coin and a silver coin. You choose a bag at random, and pick a coin from that bag. It’s a gold coin! What are the chances you picked from the bag with two gold coins?

You have 50 red balls and 50 blue balls. You can distribute them between two boxes in any way you choose. Someone will come and pick a box at random, and then pick a ball from that box at random?

A wandering magician places a freshly shuffled deck face-down on a table. She then opens a small chest full of golden coins.

One of these boxes has a prize. I told Astrid only the color of the box. I told Bill only the symbol."

A tricky puzzle involving conditional probability. Which box should you pick from?

There are 11 gumballs in a machine: 6 pink, 4 white, and 1 blue. They cost 10 cents each. You want 2 of the same colour (any colour will do), but they come out at random.

Two boys on bicycles 20 miles apart began racing directly toward each other. The instant they started, a fly on the handle of one bicycle started flying straight toward the other cyclist.

Every day you flip a fair coin until you get heads, then stop. What’s the long-run average number of flips you make per day?

Your friend puts three dice on the table with unusual numbers on their sides. Your friend then suggests a game.

Highly intelligent children tend to have friends who are less intelligent than they are. What is the most likely explanation for this?

You post a survey asking, 'Do you like surveys?' 100 people fill out the survey. 95 of them answer 'Yes'. Can you conclude that most people like surveys?

You have 5 bottles, each containing 10 pills. One of them has heavier pills. Can you find out which one?

Jack is looking at Anne. Anne is looking at George. Jack is married and George is not married. Is a married person looking at an unmarried person?

You wrap a band around the equator so that it touches the ground at all places. Then you add 10 meters to its length. How far will it rise above the ground?

You are standing at the South Pole. You walk 1 kilometer north. You turn 90 degrees and walk in a line. Will you ever reach the South Pole again?

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 prize; behind the other two, nothing.

Can you solve the coin flip puzzle? If you toss a coin 4 times, what is the most likely split between heads and tails?

Draw 2 squares inside this square to isolate all the dogs from each other.

There are three candidates in an election: A, B, and C. Most voters prefer A over B. Most voters prefer B over C. Can we conclude that most voters prefer A over C?

You are blindfolded and there are four coins in front of you. You know that two of them are heads side up and two of them are tails side up.

Binary Labs makes only two kinds of robots: truth-bots, which only tell the truth, and trick-bots, which only lie. They look identical.

You have four cookies. One of them turns mice pink an hour after they eat even one bite, but you don’t know which one! You need to figure it out in an hour.

Can you solve this math puzzle? Look at the picture and determine how much an empty jar weighs. There are multiple ways to solve this.

Three smart boys are standing in a line. Each is wearing a hat that is either red or blue, but they don’t know the color of their own hat.

Courses

Fallacy Detectors

Ages 8–12

A story-based course that teaches kids to spot logical fallacies through science-fiction videos and activities.

US$15

Social Media Simulator

Ages 9+

Teach your kids to spot misinformation and manipulation in a safe and controlled environment.

US$15

A Statistical Odyssey

Ages 13+

Learn about common mistakes in data analysis with an interactive space adventure.

US$15

Logic for Teens

Ages 13+

Learn how to make sense of complicated arguments with sci-fi themed video lessons and activities.

US$15

Emotional Intelligence

Ages 5–7

Learn to recognize, understand, and manage your emotions. Designed by a child psychologist.

US$10

Worksheets

Logical Fallacies Worksheets and Lesson Plans

Ages 8–12

Teach your grades 3-7 students about ten common logical fallacies with these engaging and easy-to-use lesson plans and worksheets.

US$10

Symbolic Logic Worksheets

Ages 13+

A 20-page worksheet pack introducing teens to symbolic logic.

US$5

A Statistical Odyssey Worksheets and Lesson Plans

Ages 13+

Turn A Statistical Odyssey into a complete 14-class unit for homeschool or classroom with these lesson plans, printable worksheets, and a cumulative assessment.

US$10

Elementary School Worksheets and Lesson Plans

Ages 7–10

These lesson plans and worksheets teach students in grades 2-5 about superstitions, different perspectives, facts and opinions, the false dilemma fallacy, and probability.

US$10

Middle School Worksheets and Lesson Plans

Ages 10–13

These lesson plans and worksheets teach students in grades 5-8 about false memories, confirmation bias, Occam’s razor, the strawman fallacy, and pareidolia.

US$10

High School Worksheets and Lesson Plans

Ages 13+

These lesson plans and worksheets teach students in grades 8-12 about critical thinking, the appeal to nature fallacy, correlation versus causation, the placebo effect, and weasel words.

US$10

Statistical Shenanigans Worksheets and Lesson Plans

Ages 13+

These lesson plans and worksheets teach students in grades 9 and up the statistical principles they need to analyze data rationally.

US$10

Printable Logical Fallacy Handbook

Ages 13+

A printable PDF explaining 20 common logical fallacies with real-world examples. Recommended for teens and adults.

US$5

Printable Logic Puzzle Cards

Ages 10+

Printable logic puzzle cards with answers and explanations. Varied levels mean they will challenge kids, teens, and even adults.

US$5

Printable Data Analysis Handbook

Ages 13+

A printable PDF explaining 8 common errors in data analysis with real-world examples. Recommended for teens and adults.

The Language of Science: Facts, Laws, and Theories

Ages 11+

This free science literacy worksheet teaches the difference between facts, laws, and theories and addresses common misconceptions. Recommended for grade 6 and up.

Printable Formal Fallacy Handbook

Ages 13+

A printable PDF explaining 6 formal fallacies with examples. Recommended for teens and adults.