Project Euler Forum

From the problem page:
"For example, if k = 6, a = 0.9 and b =  0.55, then (k·a+1)^(2) + (k·b+1)^(2) = 40.05."
but:
(k·a+1)^2 + (k·b+1)^2
=(6·0.9+1)^2 + (6·0.55+1)^2
=6.4^2 + 4.3^2 = 59.45

Am I missing something or being unbelievably thick and failing at simple arithmetic?

Good spot ! There is a mistake in the given example; it will be fixed soon.

Edit: Typos fixed. The actual values are a=0.2, b=0.85, calculated sum=42.05, sq.root=6.484...

Also, is the given expected value for 1 <= k <= 10 correct? I am consistently getting something other than the given value...though that could just be cause I am wrong .

Raichev_2 wrote:From the problem page:
"For example, if k = 6, a = 0.9 and b =  0.55, then (k·a+1)^(2) + (k·b+1)^(2) = 40.05."
but:
(k·a+1)^2 + (k·b+1)^2
=(6·0.9+1)^2 + (6·0.55+1)^2
=6.4^2 + 4.3^2 = 59.45

Am I missing something or being unbelievably thick and failing at simple arithmetic?

I also noticed the same mistake. I joined the Project Euler yesterday. At first I thought I didn't understand the task. Now it's clear.

I joined project euler a while back, but i've only been doing the first problems. reached Problem 55 but now i decided to do this problem. I'm really confused on how they calculated the expected value. Could someone post a link or atleast explain how the expected value for the example given was calculated? I'm new to the whole Uniform Distribution concept but i'm open to learn new things

Tried, gave up, took a break, tried again - I suspect I might have precision problems. I get exactly the same value for k = 10.

Can anyone confirm:

k = 1000 => 1556.17575
k = 10000 => 15688.738433

zwuupeape wrote:Tried, gave up, took a break, tried again - I suspect I might have precision problems. I get exactly the same value for k = 10.

Can anyone confirm:

k = 1000 => 1556.17575
k = 10000 => 15688.738433

k = 10000 => 15688.738431

Yeah, thanks - I got it now .

I am pretty sure I have the right idea for this one, except that my result for k up to 10 is 10.91995. My results for k up to 1000 and k up to 10000 are also similar to the ones posted above, except slightly bigger. I am pretty sure I'm doing something incredibly stupid, my hope is that by posting this it will get my mind to go in gear.

dbatche3 wrote:I am pretty sure I have the right idea for this one, except that my result for k up to 10 is 10.91995. My results for k up to 1000 and k up to 10000 are also similar to the ones posted above, except slightly bigger. I am pretty sure I'm doing something incredibly stupid, my hope is that by posting this it will get my mind to go in gear.

k=1 is a special case which needs to be handled manually

I think I figured out my problem, I was assuming that conditions in the limiting case would hold in all cases. I was wrong. Now I just need to make sure all my code is correct...

k=1 is a special case which needs to be handled manually

For future seekers of help --- this means that the numbers quoted in the earlier posts are for k=2...n, NOT 1...n.
Also, the value for 1000 should be 1556.175760...

(I spent quite some time trying to find my fundamental problem, when in fact I "only" had precision problems, because I didn't realise those values didn't include k=1)

I can't get the sample problem, and I'm not doing anything special for k=1, so I presume for now that that's effect and cause.

Can someone elaborate some more about the specialty of k=1?

Thanks.
...mrt

Very hard to elaborate on k=1, and the reason is that it would spoil the problem solution.
Try to understand what you're doing and you'll also understand immediately why k=1 is kind of "special".
Cheers,
sfabriz

Thanks. While not seeing yet what I'm supposed to be looking for, I can see how that might be so.

Asking another way, then, for 65,536 attempts, I got 491 K=1's, for an EV(1) of 0.007492. For 10^6 attempts I got 7293 K=1's for an EV(1) of .0007293. In 65,536 attempts, I got 16942 K=2's for an EV(2) of 0.517029, and for 10^6 attempts I got 259497 K=2's for an EV(2) of 0.518994.

I know this isn't how to do the final problem. 10^5 loops around 10^6 loops can't be the way. But I wonder if my built-in RAND() function is the wrong one. Are those EV() in line?

...mrt

mrtollefson wrote:Thanks. While not seeing yet what I'm supposed to be looking for, I can see how that might be so.

Asking another way, then, for 65,536 attempts, I got 491 K=1's, for an EV(1) of 0.007492. For 10^6 attempts I got 7293 K=1's for an EV(1) of .0007293. In 65,536 attempts, I got 16942 K=2's for an EV(2) of 0.517029, and for 10^6 attempts I got 259497 K=2's for an EV(2) of 0.518994.

I know this isn't how to do the final problem. 10^5 loops around 10^6 loops can't be the way. But I wonder if my built-in RAND() function is the wrong one. Are those EV() in line?

...mrt

Those are reasonable approximations of the real expected values.

I believe the values posted for k=1000 and k=10000 earlier in this thread were wrong. My AC program gets:
k=1,000 => 1556.18298
k=10,000 => 15688.74566

jpaulson wrote: Fri Nov 28, 2014 4:37 am I believe the values posted for k=1000 and k=10000 earlier in this thread were wrong. My AC program gets:
k=1,000 => 1556.18298
k=10,000 => 15688.74566

I have just completed this problem and I can confirm that these are the correct values. I'm not sure what is going on in the rest of this thread.