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# 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.

## 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

## 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