Search found 335 matches

by rayfil
Mon Jul 23, 2007 4:48 am
Forum: Number
Topic: "Summarizing" sequence
Replies: 11
Views: 3691

Re: "Summarizing" sequence

The rounded estimates were thus quite good. 8-) I had to change integers to int64 Was that really necessary? Both the length and sum are well within the int32 range. BTW, how long did your algo take for 70. The estimate for my assembly algo would be about 8 seconds. The main reason I didn't take it ...
by rayfil
Tue Jul 17, 2007 7:24 pm
Forum: Number
Topic: "Summarizing" sequence
Replies: 11
Views: 3691

Re: "Summarizing" sequence

The data from the 50th term to the 60th term provided the following ratios: 1- The average of the digits in the final string is relatively constant at 1.6895 plusmn 0.0001 2. The ratio of the sum from one term to the next is relatively constant at 1.304 plusmn 0.0005 3. This also means that the rati...
by rayfil
Tue Jul 17, 2007 6:52 pm
Forum: Number
Topic: "Summarizing" sequence
Replies: 11
Views: 3691

Re: "Summarizing" sequence

Here's a descriptive summary of my algo which you can try to implement in your own programing language. [code]//Allocate memory for two "string" buffers buf1 and buf2 (1 Mb for each buffer would be sufficient for the 50th term). One will be the source buffer and the other will be the destination buf...
by rayfil
Tue Jul 17, 2007 5:24 am
Forum: Number
Topic: "Summarizing" sequence
Replies: 11
Views: 3691

Re: "Summarizing" sequence

I agree with ThomasH's sum and string length for the 50th term. The sum of the digits in the 60th term is 21424450 (the string has a length of 12680852), and my algo in assembly took 484 ms on an old P4-1500. The size of the computing part of my app is only 150 bytes. 8-) What programming language a...
by rayfil
Mon Jun 18, 2007 6:38 pm
Forum: News, Suggestions, and FAQ
Topic: How is the ranking determined ...
Replies: 1
Views: 1717

Re: How is the ranking determined ...

within the number of problems solved? Yes. And for the same number of problems solved, the ranking is according to the date and time when the latest problem was solved. The previous ranking method (up to about a year ago) was based on a number of point assigned to each problem based on the number o...
by rayfil
Wed Jun 06, 2007 8:50 pm
Forum: Combinatorics
Topic: Minimal snooker
Replies: 3
Views: 2835

Re: Minimal snooker

Technically, the minimum winning score would be (15+2+3+4+5+6+7)/2+1 = 23 if neither player pockets a color ball after pocketing each red ball, and no foul is commited throughout the frame. However, the winning player could have pocketed only a single RED ball during the entire frame but accumulated...
by rayfil
Sun Mar 11, 2007 5:15 am
Forum: Number
Topic: sequence
Replies: 11
Views: 4791

m4
a(n)=n^2(n^2-1)/12
This one seems wrong, giving a(1)=0, while all your other equations give a(1)=1.
by rayfil
Wed Dec 27, 2006 4:10 am
Forum: Number Theory
Topic: smallest multiple of 17 (urgent! )
Replies: 6
Views: 4180

Another option you may look into is to determine the length of the recurring cycle of the reciprocal of the number. The reciprocal of 17 would be: 0.058823529411764705882352941176470588235294117647..... and you can see that the recurring cycle would be 0588235294117647 which contains 16 digits. If y...
by rayfil
Tue Oct 10, 2006 3:26 am
Forum: Geometry
Topic: Vector assistance
Replies: 3
Views: 3546

There's a lot of information about vectors on MathWorld although it may be difficult to "digest" at times. You may want to start with the following and branch out from there if it may prove to be helpful. http://mathworld.wolfram.com/DotProduct.html You could also do a search with the word "vector" ...
by rayfil
Sat May 27, 2006 1:17 am
Forum: Number Theory
Topic: Large Perfect Squares
Replies: 12
Views: 7594

I came up with that algo based on the fact that regardless of the number of fractional digits you would use for an irrational square root, multiplying it by itself will ALWAYS yield a number a little smaller than the original one. Incrementing any of the fractional digit of the square root will alwa...
by rayfil
Fri May 26, 2006 4:58 pm
Forum: Number Theory
Topic: Large Perfect Squares
Replies: 12
Views: 7594

Here's my approach to this problem. Although I have not written a specific program for it, the steps would be as follows. I have tested the procedure with my available square root extractor (which is good for ANY input and an output of up to 9999 fractional digits), and a quick algo to multiply a nu...
by rayfil
Sun May 14, 2006 4:30 am
Forum: Number
Topic: Reverse Difference
Replies: 4
Views: 2987

My approach:
It is necessary for a > b
[there4] from the units: b+10-a=4 (1)
1 must then be borrowed from the a for the 10s
and thus: a-1-b=c (2)

Adding the two equations (1) and (2) gives: 10-1=c+4
[there4]c=10-1-4=5
by rayfil
Fri Apr 14, 2006 3:45 am
Forum: Number
Topic: Log to base pi
Replies: 7
Views: 5629

How about

zero
by rayfil
Thu Apr 06, 2006 3:17 am
Forum: Number
Topic: How Likely To Divide?
Replies: 12
Views: 9995

My analysis is: All results are divisible by 1 but its probability of being the divisor is 20%. If both x and y are even, the result will be divisible by both 2 and 4. Probability is 1/2*1/2*2/5 = 10% If both x and y are odd, the result will be divisible by 2. Probability is 1/2*1/2*1/5 = 5% If both...
by rayfil
Sun Apr 02, 2006 6:24 am
Forum: Applied Mathematics
Topic: Diagnosis
Replies: 4
Views: 5069

The way I would see it is:
95% of 5% = 4.75% will test positive + 10% of 95% = 9.5% will also test positive for a total of 14.25%. The probability of those testing positive really having cancer would be 4.75/14.25 = 33.33...% (or 1 in 3)