Efficient solutions to Project Euler (mtn-i.info) problems. - rohitjha/ ProjectEuler. Hi, I'd like to solve puzzles from the ProjectEuler when I'm far away fom internet - so a complete listing of all puzzles in a single PDF file would. Project Euler: Project Euler 2: Even Fibonacci numbers. 6 . This is one of my favourite problems and as a teaser the solution can be.
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Project Euler. Steven Miller ([email protected]). (*For this problem we could go through and keep track of the multiples of. 3 and 5 and add. We can also use. The problems archives table shows problems 1 to If you would like to tackle the 10 most recently published problems then go to Recent problems. Click the. Project Euler (Mostly) in Python. Bryan Harris mtn-i.info~ brywilharris/eulerplay/trunk/files. Currently 25 Problem 1 Solution.
Does anyone know where I can find a transcript of the problems? This question appears to be off-topic.
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I threw together a little script to compile every problem together in a single flat text file, adding the attachments in a zip file. The conversion process goes to some lengths to ensure a highly readable copy.
However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! Thirty days has September, All the rest have thirty-one, Saving February alone, Which has twenty-eight, rain or shine.
And on leap years, twenty-nine. A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by How many Sundays fell on the first of the month during the twentieth century 1 Jan to 31 Dec ?
Factorial digit sum n! Find the sum of the digits in the number ! Or so I thought. Problem explicitly requires that the only red blocks you can have must appear in runs of three or more.
You can imagine what I did next. It cost me about two hours of mostly unnecessary work, an expense I would have avoided if I had never seen in the first place. It was an unlikely lesson: drawing on experience can sometimes do more harm than good. After scrapping that angle I decided to do something a bit ignoble. I decided to write some code to exhaustively spit out trinary strings, not of length 30—such a program would take weeks to run—but for small ns.
If I hit a match I might be able to steal a nice clean formula. One must use it sparingly and as a last resort.
Descent into madness A was a huge boon—rather than computing the count in Step 2 above, I could literally copy and paste the correct value from a list someone else had already generated and posted to the OEIS. And with that I was only one term away from a full solution. All that was left was to work through Step 3: counting strings just like the ones in Step 2 that also include a single L.
When you think about it, it actually seems like a trivial modification could get you from the strings that A is counting to the strings that also include a single L call them L-strings.
To get the number of L-strings, all you have to do is to take each Astring—each string of As and Os—and multiply it by the number of O-spots as opposed to A-spots , those being precisely the spots where you can put the L. So after fumbling around the OEIS for just over an hour trying to find some code or sequence or math that might get me those numbers, I was left seemingly without a way out.
But instead of dropping the idea, I decided to work it out in painstaking detail. You can see the insane work that came out of this insane project by looking at pages 1 and 2 in this PDF of scratch paper. I used a helper script to compute those subscripts as n and k increased.
Because it hit me like a ton of bricks: I should be solving this problem inductively. Think about it this way. Suppose I know how exactly how many prize strings there are for a given n. Now increment n by one.
What changes? Well, there are only three letters that can be added to a given string: O, A, and L.
If I add an L to a string that already has an L, all of a sudden that string becomes ineligible; same thing if I add an A to a prize string ending in AA. If I had an O to any string, it has no effect.