Tag Archives: triangular

The route puzzle

Posted on June 17, 2016 by Brent

While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading →

Posted in arithmetic, challenges, number theory, proof, puzzles | Tagged , , , , , , | 7 Comments

Triangular number equations via pictures: solutions

Posted on April 14, 2011 by Brent

Here are some solutions to my previous post. However, they are almost certainly not the only solutions! If you have other cool ways to visualize any of these (or any other triangular number equations) feel free to post in the … Continue reading →

Posted in arithmetic, pattern, pictures, proof, solutions | Tagged , , , | 10 Comments

Triangular number equations via pictures

Posted on March 24, 2011 by Brent

The other day I was fiddling around a bit with triangular numbers. By only drawing pictures I was able to come up with the following triangular number equations, where denotes the th triangular number (that is, the number of dots … Continue reading →

Posted in challenges, pictures, proof | Tagged , , , | 8 Comments

Triangunit divisors and quadratic reciprocity

Posted on March 20, 2011 by Brent

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading →

Posted in arithmetic, modular arithmetic, number theory, primes, proof | Tagged , , , , | 5 Comments

Triangunit divisors

Posted on March 1, 2011 by Brent

Here’s a neat problem from Patrick Vennebush of Math Jokes 4 Mathy Folks: Append the digit 1 to the end of every triangular number. For instance, from 3 you’d get 31, and from 666 you’d get 6,661. Now take a … Continue reading →

Posted in number theory, pattern, puzzles | Tagged , , , , | 9 Comments

Math Teachers at Play #21

Posted on December 19, 2009 by Brent

Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading →

Posted in fibonacci, links, number theory, puzzles | Tagged , , , , , , | 13 Comments