No fancy-pants recursion or math short-cuts here, just a straight forward logic problem. The only "trick" here is to realize that since a <e; b < c, we only need to check values of a and b up to 499.

I'm sure you could whittle that number down by crunching the numbers, but it's good enough for me!

Problem 39

For which value of p 1000, is the number of solutions maximised?

counts = {}
counts.default = 0

(1..499).each do |a|
  (a..499).each do |b|
    break if a + b > 500
    c = Math.sqrt(a**2 + b**2)
    next unless c.denominator == 1
    counts[a + b + c] += 1
  end
end

sorted = counts.sort { |a, b| a[1] <=> b[1] }

puts sorted.last[0]

                          

It helps smooth frustrations, keeps me awake, and provides "color" for my day. I want my office to feel like a 1960's Sci-Fi movie!

Most importantly, the music helps me "flow" by drowning out the regular office clatter and bang-clangery.

I used to be over by the window, and I could see the squirrels...

Admittedly, I tend to "burn out" early on music, but 2,000+ hours of work/year will eventually tire even the most stalwart listener and extensive collection. Especially since a lot of the music I like "in real life" doesn't mesh well with concentrating. I usually find lyrics to be too distracting.

Since audiobooks and podcasts have taken over my ipod, I do almost all of my music listening at work. This has introduced a strange and large gap between the music that I used to like and the music I actually listen to.

Although I love it, my office is a no Kanye zone!

My office is a No Kanye Zone

Since I require so much "background" music, services like and Pandora are perfect fit for me. I'm constantly tweaking my stations, but here's my current fave for work:

My favorite Pandora Station:
Programming Music: Boards of Mercury Circles

And here's a few youtubes of songs you might hear on that station:

                          

The real trick here is to cut down on the numbers you check. Since the problem gives you 918273645 as an example we know the answer must be greater than or equal to it...meaning we only need to check digits that start with 9!

I don't actually do it because I couldn't figure out an elegant way to do, but it runs in just a few milliseconds so it's fast enough in my book.

Another important factor to note is that you only need to check numbers up to 9_876 since this is the first 'half' of the largest pandigital possible.

Those two tricks will cut down the calculations you need to run to just a few thousand.

Problem 38

What is the largest 1 to 9 pandigital 9-digit number that can be formed as the concatenated product of an integer with (1,2, ... , n) where n 1?

def get_pandigital? n
  nums = []
  (1..9).each do |digit|
    nums += (n * digit).to_s.split ''
    return 0 if nums.size != nums.uniq.size || nums.include?('0')
    return nums.join('').to_i if nums.size == 9
  end
end

solution = 0

(9..9_876).each do |n|
  # could do better by only looking at 9's!
  result = get_pandigital? n
  if result > solution
    solution = result
  end
end

puts solution

Check out all of my solutions on bitbucket!

                          

BAM!

Problem 37

The number 3797 has an interesting property. Being prime itself, it is possible to continuously remove digits from left to right, and remain prime at each stage: 3797, 797, 97, and 7. Similarly we can work from right to left: 3797, 379, 37, and 3.

Find the sum of the only eleven primes that are both truncatable from left to right and right to left.

load 'prime_generator.rb'

def prime? n, truncate
  return false if !$primer.is_prime?(n)
  return true if n < 10
  prime? truncate.call(n), truncate
end

left = Proc.new { |n| n / 10 }
right = Proc.new { |n| n % 10**Math.log10(n).to_i }

$primer = Prime_Generator.new 3_797
n, sum, found = 0, 0, 0

while found < 11 do
  if (n += 1) > 10 && prime?(n, left) && prime?(n, right)
    found += 1
    sum += n
  end
end

puts sum

Also, I've finally moved my project euler solutions over to bitbucket. Long live Mercurial!

                          

Read more about it, and check it out yourself: Otomato

The rules for the automation are simple, but the hypnotic patterns that emerge are truly beautiful and interesting. The user interface is both easy and fun to use, and it does a great job of showing the simple beauty of what you're listening to.

The music reminds me a lot of one of my favorite bands Boards of Canada, so if like the sound of this then check them out, it makes for great programming music.

                          

Both completely free events, and both were fun, inspiring, and eye-opening in their own ways. I came away feeling inspired, invigorated, and with a couple of new nerdy (read: cool) t-shirts!





Orlando CodeCamp was incredibly educational and informative with it's tech-heavy, hour-long formal presentations. I can't imagine all the hard work put in by the speakers and volunteers to have such a large and superior quality event run, and run so smoothly.

There was a definite collegial vibe (taking place at the beautiful Seminole County College campus didn't hurt!) but oh how I wish my university experience was as interesting, efficient, relevant, and productive.

Special thanks to the ONETUG president Esteban Garcia for patiently and thoroughly answering all my inane TFS questions. I've avoided TFS talks in the past because I thought they would be boring, but boy was I wrong! It really cool to see everything up and integrated like that!

Also another special thanks to SubMain for the CodeIt.Right licensce I won. I'm already putting it to good use!

If CodeCamp felt like school, then BarCamp felt more like...Woodstock. The event took place in the Wall Street Plaza, with talks taking place in local venues like One-Eyed Jacks, Slingapours, and The Gibson Showroom. The presentation times and topics were updated throughout the day on a giant white board, and there was a great little mobile site for keeping track of the ever evolving schedule the on your iPhone. (I'm an Android fanboy, but I don't think I've ever seen so many Apple products in one place before!)

The talks ranged from the technical to the artistic to the entrepreneurial, and there were strong revolutionary, community and outside-the-box undercurrents behind most talks.

The session that most picqued my interest was done by Stan Schultes, Microsoft MVP and organizer of the BarCamp Sarasota. He led a 'birds of a feather' style centered around software start-ups, and what cities like San Francisco, Boston and New York have that we in the "Greater Central Florida Region" don't....and how we can organize to fix it!

The biggest take-away for me however is getting to see and meet so many inspired and passionate makers, shakers and enthusiasts out there trying to make a difference.

Photo Credit: Nick Pettit

I'm looking forward to checking out recently discovered entities like Orlando Coding Dojo, Urban ReThink, and Familab events in the near future.

Big shout out to ONETUG, ORUG, and Envy Labs for being such big drivers behind these events and a big thanks to all the organizers, sponsors and community. Fantastic job!

Oh, and I almost forgot to mention the best part about these two events: They're recurring!

I'm looking forward to seeing you all again soon!

                          

Well...

I've been nooking CLR via C# and it's a fantastic read for anyone who wants to 'get serious' about .Net. The book's so crammed full of good information it's hard not to gush, but I digress.

I was nooking, you see, and I came across this recommendation:

"Use signed data types (such as Int32 and Int64 instead of unsigned numeric types such as UInt32 and UInt64) wherever possible."

Jeffrey Richter continues:

"This allows the compiler to detect more overflow/underflow errors. In addition, various parts of the class library (such as Array's and String's Length properties) are hard-coded to return signed values, and less casting is required as you move these values around in your code."

Casting is ugly, no argument there but I don't care much about the overflow/underflow errors. I generally don't enable overflow checking, there's no political statement here, it's just never come up.

And it still feels wrong for me to declare a value signed when I know that it shouldn't be.

(Richter recommends enabling checking for debug builds, and disabling for release. Sound advice!)

But here's real the kicker for me:

In addition, unsigned numeric types are not CLS-compliant.

Doh. I did a bit of searching to try and track down why it's not part of the CLS, and I found that Brad Abrams expresses it best in this post:

"The general feeling among many of us is that the vast majority of programming is done with signed types. Whenever you switch to unsigned types you force a mental model switch (and an ugly cast). In the worst cast you build up a whole parallel world of APIs that take unsigned types. The value of avoiding the '< 0' check is not worth the inclusion of generics in the CLS"

Alright, I give in. I'm apparently in the minority, these guys are way smarter than I am, and it is easier, if not more concise. So it goes.

Goodbye for now uint, you'll always hold a positive place in my heart.

Just like Weezer:

                          

Problem 35

How many circular primes are there below one million?

require 'prime_generator'

primer = Prime_Generator.new 1_000_000

def is_rot_prime? primer, chars
	chars.size.times do |i|
		chars = Array.new(chars.size) { |i| chars[i - 1] }
		return false if !primer.is_prime?(chars.join("").to_i)
	end
	true
end

count = 0
primer.stack.each do |n|
	count += 1 if is_rot_prime? primer, n.to_s.split("")
end

# subtract 1 because "1" doesn't count
puts count - 1

Speaking of the rotation, the ruby array initialize methods and negative indexers make it a cinch to rotate. How cool is this?

chars = Array.new(chars.size) { |i| chars[i - 1] }

                          

The first hurdle was figuring out the upper bound. After scratching around in my notebook, I figured any number I would be looking for would have 7 digits or less. That gives us an upper bound of 9! * 7.

The second hurde took me much, much longer to figure out.

Here's the secret: 0! = 1

I had taken it for granted that 0! would (of course!) be 0, and I had pre-filled my cache with the number 0. I went round, and round, and round, and round, and round, and round before figuring out (quite accidentally) my error.

It doesn't make any sense to me, but you can't argue with math!

Problem 34

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

# cache the digit factorials
factorials = [1]
(1..9).each do |i|
	factorials.push(i * factorials.last)
end

result = 0
(3..2_540_160).each do |n|
	sum = n.to_s.split("").inject(0) do |sum,n|
		sum + factorials[n.to_i]
	end
	result += n if n == sum
end
puts result

Runs in just under a minute

                          

Problem 36

Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2.

def palindrome? s
	s == s.reverse
end

sum = (1..1_000_000).inject(0) do |sum, n|
	sum += palindrome?(n.to_s) && palindrome?(n.to_s 2) ? n : 0
end

puts sum