Project Euler Forum

The same idea works for this case too. If I'm not wrong, you only have to learn to use the idea from Problem 1 (View Problem).

It takes a simple brute force to verify that the intended process is 112233. The source of confusion is maybe because of the following words: “As before each person takes a random slip from the hat that does not contain their name. Then they do the same process again so that they end up with two sli...

A simple idea is to convert them into bivariate generating functions.. For example, define

$\displaystyle F(x, y) = \sum_{n,k \geq 0}C(n,k)x^ny^k$

Use the recurrence you have quoted to arrive at an expression for $F(x,y)$. That should hopefully give you the required $O(n)$ algo.

It's very early to post values hacatu. Please keep working on the problem and remove the values. Possibly, someone will reply and you can get the chat in a private 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 o...

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...