Illustration by Guillaume Kurkdjian
Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either, and you may get a shoutout in the next column. Please wait until Monday to publicly share your answers! If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter or This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
Riddler Express
Earlier this week, I had the pleasure of attending the MOVES conference in New York City, hosted by the National Museum of Mathematics. The opening keynote, “How to Invent Puzzles,” was delivered by puzzle master Scott Kim. In particular, his cuisenaire-rod puzzles got me thinking. …
A hexomino is a shape made by six identical, nonoverlapping squares that are connected by edges. Some hexominoes, like the one shown below, can be decomposed into an array of three squares, an array of two squares and an array of one square.
How many distinct hexominoes can you find that cannot be decomposed into arrays of three, two and one squares? For the purposes of this riddle, two hexominoes are considered equivalent if they can be turned into one another by rotation and/or reflection.
Riddler Classic
From Andrew Lin comes a game for getting yourself home:
You are stranded in a casino (lucky you!) and need to purchase a flight home. Flights cost $250, but you have only $100 at the moment. However, as I just said, you’re in a casino! Surely, you can gamble your way to $250.
The casino has a game called “Riddler’s Delight,” in which you can bet any amount of money in your possession for an even greater amount of money. You can even bet fractional (i.e., you can bet fractions of a penny), irrational or infinitesimal amounts if you so desire.
The catch is that the odds are not in your favor. In Riddler’s Delight, whenever you bet A dollars in an attempt to win B dollars (with B > A), your probability of winning is not A/B, which you would expect from a fair game. Instead, your probability of winning is always 10 percent less, or 0.9(A/B).
What should your betting strategy be to maximize your probability of getting home, and what is that probability?
Solution to last week’s Riddler Express
Congratulations to
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