Project Euler Forum

Hi yourmaths, "chosen uniformly" here means we choose one triple from among those which satisfy the limits AND the GCD condition. If you consider only the limit, you'll have a total of $\displaystyle \binom{100}{3}$ triples to choose from. But we will have lower number of triples because of the GCD ...

Hi vamsikal3, It's been a while we had a chat. Hope you are doing good.. Regarding the discussion here, I think you've put it nicely here. ... So, if unlocking problems that I cannot solve after spending a few days on it helps me learn/understand new mathematics or programming techniques. I believe ...

Great feature euler. Came in handy today.. A big thanks!!

The undocumented Algebra`MatrixPowerMod. Useful in many PE problems.

This post has a lot people sharing their experience at your (or our) stage.

I've also listed some topics in the above thread which can help in solving many PE problems.

Happy Solving!!

Hi, For some reason, I can't login to my account. PE says 'Username not known'.

Can anyone let me know why this is happening?

It's just a mathematical description RishadanPort. To make it more abstract, if you randomly select a point inside a right angled triangle and randomly choose some direction to draw a line (starting from the point we chose), what is the probability that the line intersects the hypotenuse?

We cannot make two consecutive posts in the same solution forum. I think you should be able to edit your post and add the content in the same post.

671 Hi All, Tiling which are identical after rotating the loop about its axis considered different? Only if I consider them different, I get F_4(3) = 104. Else am stuck at 92. I'm not sure whether 'reflecting horizontally or vertically would give a different tiling, these tilings are to be counted ...

Hi mdean,
If you could PM your value, I can confirm it.

The kudos count is aligned properly now. Kudos for that euler...

Many thanks to the PE team for the new style. The site looks great with the new styling.

The only issue that I saw was as that of MHealy. For non-permananent posts, the kudos are slightly mis-aligned in Chrome.

Truly appreciate the hard work in getting PE a new style.

For me the problem appears in Chrome but not in IE...

Now I have this problem...

If I try to view my posts from 173-180, then am directed to the sign-in page even though am not signed-out of PE.

Like v6ph1 said, if you are looking for online compilers, repl is my favourite..

I changed the code to remove the loop-checking and use modified-step values but still no improvements in timing. For example, the mod-2 version takes ~ 75 secs to list all primes upto 10^8, the mod-6 version takes ~ 85 secs whereas the step-adjusted-mod-6 version takes ~ 95 secs. step-adjusted-mod-6...

Thanks v6ph1. I too arrived at the same loop for making the program slow. But I think it may be slightly different. Rather than the loop checking, I think the runs more often as the chance of hitting the numbers with mod in the given set becomes low. That I think is the trade-off in the higher mod v...

Hi all, I recently saw a post on an Infinite Prime Number Generator on Stack Exchange given below. from itertools import count from timeit import default_timer start = default_timer() # ideone.com/aVndFM def postponed_sieve(): # postponed sieve, by Will Ness for c in (2, 3, 5, 7): # original code Da...

@ jaap , I think you did all the heavy lifting leaving just the algebra to me. The key to solving this problem is to pick the 'central angle' as the variable of interest. Though the 'cubic' approach ended nowhere, it reminded me of the trick of evaluating $\sin(\pi/5)$ exactly, which I kinda used to...

... It is straightforward to see that: A1A2 = 2sin(x) A1A3 = 2sin(2x) A1A4 = 2sin(3x) From here, we have, $\displaystyle\frac{1}{\sin x}=\frac{1}{\sin 2x}+\frac{1}{\sin 3x}$ $\displaystyle\sin 2x=\frac{\sin x \sin 3x}{\sin 3x-\sin x}=\frac{\sin x \sin 3x}{2\sin x-4 \sin^3 x}=\frac{\sin x\sin 3x}{2 ...