# Category Archives: Test your intuition

## TYI 26: Attaining the Maximum

(Thanks, Dani!) Given a random sequence , ******, , let . and assume that .  What is the probability that the maximum value of is attained only for a single value of ? Test your intuition: is this probability bounded … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged | 21 Comments

## TYI 25: The Automorphism Group of the Symmetric Group

True or False: The group of automorphisms of the symmetric group , n ≥ 3 is itself.

## Test your intuition 24: Which of the following three groups is trivial

Martin Bridson We have three finitely presented groups A is generated by two generators a and b and one relation   B is generated by three generators a, b, c and three relations ,    . C is generated by four generators a, b, c, d … Continue reading

## Test Your Intuition (23): How Many Women?

How many women can you find on this poster announcing the 25th Jerusalem School in Economics Theory devoted to Matching and Market Design? Please respond to the poll:

Posted in Economics, Test your intuition, Women in science | Tagged | 5 Comments

Indeed, most people got it right! Bundling sometimes increases revenues, sometimes keeps revenues the same, and sometimes decreases revenues. In fact, this is an interesting issue which was the subject of recent research effort. So here are a few … Continue reading

## Test your intuition (22): Selling Two Items in a Bundle.

One item You have one item to sell and you need to post a price for it. There is a single potential buyer and the value of the item for the buyer is distributed according to a known probability distribution. It … Continue reading

Posted in Economics, Test your intuition | Tagged | 1 Comment

## Auction-based Tic Tac Toe: Solution

Reshef, Moshe and Sam The question: (based on discussions with Reshef Meir, Moshe Tennenholtz, and Sam Payne) Tic Tac Toe is played since anciant times. For the common version, where the two players X and O take turns in marking … Continue reading

## Test Your Intuition (21): Auctions

You run a single-item sealed bid auction where you sell an old camera. There are three bidders and the value of the camera for each of them is described by a certain (known) random variable: With probability 0.9 the value … Continue reading