Category Archives: challenges

Idempotent endofunctions

Posted on April 17, 2009 by

Via Topological Musings comes another neat little counting problem. A function is idempotent if applying it twice gives the same result as applying it once: that is, for any input x. Endofunction is just a fancy way of talking about … Continue reading →

Posted in challenges, counting | Tagged , , | 8 Comments

Distributing cookies

Posted on April 1, 2009 by

Here’s a neat problem I saw in a recent post by Steven Miller on the Williams College math department blog. The problem comes from an old Putnam competition, one of the most prestigious college mathematics competitions. (It’s also one of … Continue reading →

Posted in challenges, counting | Tagged , , | 23 Comments

Chessboard counting: solutions and further challenges

Posted on March 30, 2009 by

And now for some solutions to the chessboard counting challenges. The first challenge was to count the number of squares of any size on an 8×8 chessboard. The key here (as with many counting problems) is to break the problem … Continue reading →

Posted in challenges, counting, solutions | Tagged , , , , | 2 Comments

Chessboard counting

Posted on March 13, 2009 by

I am currently doing a unit on combinatorics (the mathematical study of counting) with my precalculus students, and I was inspired to post a few counting-themed challenge problems for your enjoyment. (Also, it’s my spring break!) As you probably know, … Continue reading →

Posted in challenges, counting | Tagged , , , , | 10 Comments

Carnival of Math #48, and Monday Math Madness #25

Posted on January 31, 2009 by

The 48th Carnival of Mathematics is posted at Concrete Nonsense. My favorite posts include Foxmath’s post about a strange iterated sequence involving pi and this amazing picture of a fractal cabbage. Also near and dear to my heart is Mark … Continue reading →

Posted in challenges, counting, famous numbers, fractals, links | Tagged , , , , | 1 Comment

Predicting Pi

Posted on October 1, 2008 by

Inspired by a recent post over at Foxmaths!, here’s an interesting challenge question for you to think about: Suppose I give you the sequence of integers , and so on, where denotes the greatest integer less than or equal to … Continue reading →

Posted in challenges, pattern, sequences | Tagged , , , | 3 Comments

Rational and irrational numbers

Posted on August 31, 2008 by

Most readers of this blog probably know what a rational number is: it’s a number that can be represented as a ratio (hence rational) of two integers. In other words, a fraction. Examples are 3/4, 99/2, and -20837/231, and even … Continue reading →

Posted in algebra, challenges, number theory, proof | Tagged | 11 Comments

Change probabilities

Posted on June 9, 2008 by

Hello, dear reader! If you are a new reader, welcome! (I know there is at least one of you—thanks to commenter sg211 for prompting me to post again. =) I must apologize for dropping the ball on writing up the … Continue reading →

Posted in challenges, counting, probability | 17 Comments

Monday Math Madness!

Posted on April 28, 2008 by

Quan, Daniel, and Sol, from blinkdagger and Wild About Math!, have teamed up to create a fun math contest, Monday Math Madness. Every other week, they post a math problem; after one week, a winner is randomly selected from among … Continue reading →

Posted in challenges, links, number theory | 2 Comments

Challenge #12: sums of powers of two

Posted on April 18, 2008 by

A few interesting problems for you to think about: Given a positive integer n, in how many ways can n be written as a sum of powers of two, when each power is allowed to occur at most once? For … Continue reading →

Posted in challenges, counting, pattern | Tagged , , , | 18 Comments