Let n be a positive integer. Prove that n! + 1 is composite for infinitely many values of n.
via Nick's Mathematical Puzzles: 111 to 120.

## Post Archives from the ‘Puzzles’ Category

## Aces in Bridge Hands

Someone deals you a bridge hand 13 cards from a regular deck of 52 cards. You look at the hand and notice you have an Ace and say “I have an Ace”. What is the probability that you have another Ace?The cards are collected and different hand is dealt. This time you look at your hand and state “I have the Ace of Spades” which …

**Continue reading the story**"Aces in Bridge Hands"## De Bruin Card Trick

A dealer(magician) starts with 16 cards on a deck arranged in some particular order. 4 people are seated in a table around the magician. The magician asks each person in turn to cut the deck at any particular point. Then he distributes the top 4 cards one at a time to each person in the table. Then he concentrates for a while. Since the mental …

**Continue reading the story**"De Bruin Card Trick"## Fermat Theorem Puzzle

A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises …

**Continue reading the story**"Fermat Theorem Puzzle"## Is Axiom of choice correct?

**Puzzle #0:**There are people in a line, and each has a number on his hat. Each player can look to the numbers of the players in front of him. So, if is the number of player , then player knows . Now, from …

**Continue reading the story**"Is Axiom of choice correct?"

## Beat your friend at a casino

Suppose your friend invests $1 in a casino and earns $X, where X is a Random variable with mean 1, i.e. E[X]=1. Suppose you know the cdf F(x) of the random variable X. Find the cdf of a random variable Y with mean 1 (E[Y]=1) so as to maximize .
For hint: View comments on this article.
Acknowledgement: Thanks to the late prof. Thomas Cover for sharing …

**Continue reading the story**"Beat your friend at a casino"## Yue's "swap" problem

Given a regular 13-gon, a red-blue coloring of the vertices is said to be "symmetric" if there exists an axis of symmetry which passes through the center of the 13-gon. A "swap" is an operation in which we exchange the colors of any two vertices. I claim that any red-blue coloring of the vertices is at most one swap away from being symmetric. Prove/disprove my claim.