##### Parrondo's paradox

**Parrondo’s paradox**, a paradox in game theory, has been described as: *A combination of losing strategies becomes a winning strategy*. It is named after its creator, Spanish physicist Juan Parrondo, who discovered the paradox in 1996. A more explanatory description is:

*There exist pairs of games, each with a higher probability of losing than winning, for which it is possible to construct a winning strategy by playing the games alternately.*

Parrondo devised the paradox in connection with his analysis of the Brownian ratchet, a thought experiment about a machine that can purportedly extract energy from random heat motions popularized by physicist Richard Feynman. However, the paradox disappears when rigorously analyzed.

Parrondo’s paradox is used extensively in game theory, and its application in engineering, population dynamics, financial risk, etc., are also being looked into. Parrondo’s games are of little practical use such as for investing in stock markets as the original games require the payoff from at least one of the interacting games to depend on the player’s capital. However, the games need not be restricted to their original form and work continues in generalizing the phenomenon. Similarities to volatility pumping and the two-envelope problem have been pointed out. Simple finance textbook models of security returns have been used to prove that individual investments with negative median long-term returns may be easily combined into diversified portfolios with positive median long-term returns. Similarly, a model that is often used to illustrate optimal betting rules has been used to prove that splitting bets between multiple games can turn a negative median long-term return into a positive one.

##### Impossible Interview Questions From Facebook, Goldman, and others

**Procter & Gamble:** Sell me an invisible pen.

**Facebook:** Twenty five racehorses, no stopwatch, five tracks. Figure out the top three fastest horses in the fewest number of races.

**Citigroup: **What is your strategy at table tennis?

**Google:** You are climbing a staircase. Each time you can either take one step or two. The staircase has *n* steps. In how many distinct ways can you climb the staircase?

**Capital One: **How do you evaluate Subway’s five-foot long sub policy?

**Gryphon Scientific: **How many cocktail umbrellas are there in a given time in the United States?

**Enterprise Rent-A-Car****: **Would you be okay hearing “no” from seven out of 10 customers.

**Goldman Sachs: **Suppose you had eight identical balls. One of them is slightly heavier and you are given a balance scale. What’s the fewest number of times you have to use the scale to find the heavier ball?

**Towers Watson: **Estimate how many planes are there in the sky.

**Lubin Lawrence: **If you could describe Hershey, Godiva and Dove chocolate as people, how would you describe them?

**Pottery Barn: **If I was a genie and could give you your dream job, what and where would it be?

**Kiewit Corp.: **What did you play with as a child?

**VWR International: **How would you market a telescope in 1750 when no one knows about orbits, moons etc.

**Diageo North America: **If you walk into a liquor store to count the unsold bottles, but the clerk is screaming at you to leave, what do you do?

**Brown & Brown Insurance: **How would you rate your life on a scale of 1 to 10?

**Jane Street Capital****: **What is the smallest number divisible by 225 that consists of all 1’s and 0’s?

**UBS: **If we were playing Russian roulette and had one bullet, I randomly spun the chamber and fired but nothing was fired. Would you rather fire the gun again or respin the chamber and then fire on your turn?

**Merrill Lynch: **Tell me about your life from kindergarten onwards.

**Susquehanna International Group: **Five guys, all of different ages, enter a bar and take a seat at a round table. What is the probability that they are seated in ascending order of age?

Tell me in 30 seconds or less your best estimate of how many animals (multi-cell and more complex) have ever lived and died on this planet?

##### Riddle me this…

A couple lives in city A and the wife works in city B (the husband works at home). Every day the wife takes the bus at 4 PM back from city B to city A and the husband comes to pick her at the bus station and they go home (it is unknown when she gets to city A but it is in the same time every day).

The husband is so good in timing this that he knows exactly when to leave home in order to pick his wife at the exact time that she gets off the bus in city A.

One day the wife took the bus at 3 instead of 4 and as a consequence got to city A an hour before the regular time. It was a nice day so she decided not to call her husband but to start walking in the direction of their house.

Her husband didn’t know anything about this and left at his regular time to pick her up. On the way to the bus station he saw her, picked her up and they both returned home 20 minutes earlier than usual.

**The question is: How long did the wife walk before she was picked up?**