# Category Archives: solutions

## Challenge #12 solution, part I

I’ll begin by providing an answer to the first of the three questions I posed in a previous post.

Posted in counting, pattern, proof, solutions | Tagged | 8 Comments

## Perfect numbers, part III

This is the last in a series of posts about perfect numbers. A quick recap of the series so far: in part I, I defined perfect numbers as positive integers n for which , where denotes the sum of the … Continue reading

Posted in algebra, number theory, open problems, primes, solutions | 11 Comments

## Nuclear Pennies Game: Solution

It seems that everyone with a blog is always apologizing for not posting in a while, as if this has somehow inconvenienced their readers. Of course, with the magic of feed readers, email notifications, and the like, this is not … Continue reading

Posted in games, links, solutions | Tagged , , , | 1 Comment

## Challenge #10 Solution

Have you tried solving Challenge #10 yet? Go try it first if you haven’t. It’s not too hard, I promise!

Posted in famous numbers, golden ratio, proof, solutions | 3 Comments

## Challenge #9 Solution

In Which Our Hero (You) Discovers Several Methods of Proving a Combinatorial Identity Involving Pascal’s Triangle (Read Challenge #9 first if you haven’t already…)

Posted in counting, pascal's triangle, proof, solutions | 4 Comments

## Challenge #8 solution

…in which you were asked to find a formula for , the nth triangular number.

Posted in famous numbers, solutions | 6 Comments

## Challenge #5 Solution

Okay, time for a solution to Challenge #5…

Posted in famous numbers, golden ratio, solutions | Comments Off on Challenge #5 Solution

## Challenge #4 Solution, Part II

But wait! What happened to Part I, you ask!? Well, let’s play the Multiple Choice Game! (a) There is no Part I. (b) There USED to be a Part I, but it disappeared. (c) Part I will come later. Haven’t … Continue reading

Posted in sequences, solutions | Comments Off on Challenge #4 Solution, Part II

## Challenge #3 Solution

Solutions to Challenge #3 follow. If you absolutely must read the solutions without attempting the challenge, I certainly can’t stop you. But Santa Claus knows.

Posted in sequences, solutions | 2 Comments

## Challenge #2 Solution

And here are the solutions to Challenge #2…

Posted in infinity, solutions | 4 Comments