Category Archives: challenges

Monday Math Madness #31

This week’s Monday Math Madness is a nice little problem involving complex exponentiation. Go check it out, and maybe win a prize!

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Idempotent endofunctions

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

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

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

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Chessboard counting

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

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

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Predicting Pi

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

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

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!

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