# Category Archives: Brain Teaser

## Q: What fair dice can be simulated by adding up other dice?

The original question was: The five platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron) are often used in games to make 4, 6,8,12, and 20-sided dice respectively. However, if you renumber the dice using nonnegative whole numbers you can create … Continue reading

## Learning intro number theory

Physicist: We occasionally get questions about free learning resources.  Khan academy is excellent, and if you poke around you can find a smattering of free class notes and text books, but generally speaking the more more detailed/advanced the material, the … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 5 Comments

## Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall?

Physicist: This is a beautiful question, in a small part because it’s an interesting thought experiment with some clever math, but mostly because of all the reasons it couldn’t be done and wouldn’t work.  Right off the bat; clearly a … Continue reading

Posted in -- By the Physicist, Brain Teaser, Physics | 87 Comments

## Q: How many mathematicians/physicists does it take to screw in a light bulb?

Mathematician: Theorem (Bulb Screwing) It only takes one mathematician to screw in a light bulb. Proof: Let the “bulb screwing number” of a profession , be the minimum number of people of profession that must be assembled to screw in … Continue reading

## Q: Why is it that (if you exclude 2 & 3) the difference between the squares of any two prime numbers is divisible by 12?

Physicist:  That’s a really cool property! Every prime number (other than 2 and 3) can be written in the form 6j+1 or 6j+5.  For example, 17 = 6(2)+5 and 31 = 6(5)+1. This is because numbers of the form 6j, … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 6 Comments

## Q: How do “Numerology Math Tricks” work? (adding digits and tricks with nines)

The original question was: Please help me solve this math card trick, I do not understand how it works: If you take a deck of 52 cards and split it into any number of piles (lets say 3) and count … Continue reading

Posted in -- By the Physicist, Brain Teaser, Math, Number Theory | 10 Comments