Forehead numbers brain teaser | Puzzles | Math for fun and glory | Khan Academy

TL;DR

Three perfect logicians with numbers painted on their foreheads try to deduce what their own number is through logical deduction.

Transcript

This is another brain teaser that deals with people trying to logically deduce what's on their forehead. And it's called the Forehead Number Game. So what's going to happen is I guess you could say the god of brain teasers is going to get three people in a room together. Once again, these three people are perfect logicians. Which means they have in... Read More

Key Insights

• 👾 The game involves three perfect logicians with unique numbers painted on their foreheads.
• 🍹 One of the numbers is the sum of the other two.
• #️⃣ The logicians can see the numbers on the other foreheads but not their own.
• 🧑 Deductions are made based on the inability of each person to determine their own number.

Questions & Answers

Q: How do the three perfect logicians know that their numbers are unique?

The game master told them that the numbers are unique, meaning no two numbers are the same.

Q: Why do the logicians paint the numbers on their foreheads?

They paint the numbers on their foreheads because they cannot see what number is on their own forehead but can see the others'.

Q: Why does the person with the number 20 on their forehead not immediately know their number?

The person with the number 20 sees the numbers 30 and 50 on the other foreheads but cannot determine their own number with that information alone.

Q: How does the person with the number 20 on their forehead figure out their number?

When the person with the number 20 sees that the person with the number 10 cannot immediately determine their own number, they deduce that their number must be 50.

Summary & Key Takeaways

• Three perfect logicians have numbers painted on their foreheads and are told that one of the numbers is the sum of the other two.

• Each person can see the numbers on the foreheads of the other two but not their own.

• After going through a series of deductions, the person with the number 20 on their forehead realizes their number is 50.