Search found 24 matches

by wwtucker
Sun Jul 16, 2006 7:13 am
Forum: Recreational
Topic: Doctor's Advice
Replies: 8
Views: 5690

My favorite:
"I could tell you, but then I'd have to bill you."
by wwtucker
Sat Jun 17, 2006 8:34 pm
Forum: Number
Topic: Perfect Square With All The Same Digit Does Not Exists?
Replies: 3
Views: 2463

Thanks. Welcome to the forum.
by wwtucker
Sat Jun 17, 2006 12:41 pm
Forum: Number
Topic: Perfect Square With All The Same Digit Does Not Exists?
Replies: 3
Views: 2463

Brute force... We know that a number with all digits the same can be expressed as d x 11...1 with d an integer from 1 to 9. This immediately tells us that d cannot be 2,6,8 as this would require 11...1 to be divisible by the "missing" factor of 2. In addition, we can eliminate the cases where d=1,5,...
by wwtucker
Fri Apr 21, 2006 8:28 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 009
Replies: 47
Views: 14034

Here's a way of explaning the problem without giving away and hints toward the solution. We want positive integers: a,b,c such that a+b+c=1000 and a 2 +b 2 =c 2 . It is clear by inspection that there are only a finite number of possibilities - the problem statement claims that there is only one set ...
by wwtucker
Fri Apr 14, 2006 8:27 pm
Forum: Number
Topic: For what value of n does 1/1+1/2+1/3+...1/n exceed a value?
Replies: 6
Views: 4841

The series is limited above and below by log functions.

A "quick and dirty" approximation would be 2.45+log(n+.5)-log(6.5).
by wwtucker
Tue Apr 11, 2006 9:39 am
Forum: Geometry
Topic: Running in a field
Replies: 5
Views: 5365

Looks good. So what's going on as b approaches a? (this is the reason for posing part b), although I'm actually having trouble getting an exact answer myself :oops:.)
by wwtucker
Tue Apr 11, 2006 5:55 am
Forum: Number
Topic: Number of digit in factorial
Replies: 9
Views: 7641

The key is that the number of digits of n! is going to be equal to int(log 10 n!)+1. The approximation tells you how to take the log of n!. It is an approximation, but for just needing to know the number of digits, it's probably fine. In fact, for your purposes, it probably works better for larger n.
by wwtucker
Tue Apr 11, 2006 4:35 am
Forum: Number
Topic: Number of digit in factorial
Replies: 9
Views: 7641

A good starting point is

n! [approx] nn/en

You might want to check out http://mathworld.wolfram.com/StirlingsA ... ation.html.
by wwtucker
Sun Apr 09, 2006 9:37 am
Forum: Geometry
Topic: Running in a field
Replies: 5
Views: 5365

You are making the assumption, perhaps correct, that the only two ways in which it makes sense to run are (immediately) into the field or along the path and then at a right angle into the field. What about running along the path and then running into the field at a (non-right) angle?
by wwtucker
Fri Apr 07, 2006 11:18 pm
Forum: Number
Topic: How Likely To Divide?
Replies: 12
Views: 9304

It would have worked if we still used base 60...
Begoner wrote:I think your solution is correct, but...
Whoops. Fixed it now
by wwtucker
Fri Apr 07, 2006 11:00 pm
Forum: Number
Topic: How Likely To Divide?
Replies: 12
Views: 9304

Re: How Likely To Divide?

waldrop [quote="waldrop"] a third of all numbers can be divided by 3[/quote] You're assuming an even distribution for the sum of the squares of two randomly chosen integers. Begoner [quote="Begoner"] So the set of all the square numbers is {0, 1, 4, 6, 5, 6, 9, 4, 1} and they all occur with equal fr...
by wwtucker
Fri Apr 07, 2006 8:41 pm
Forum: Geometry
Topic: Running in a field
Replies: 5
Views: 5365

Running in a field

I am in the middle of a field, at the intersection of two paths. One runs (exactly) north-south and the other (exactly) east-west. (In other words, I am at the origin on the x-y plane.) I can run along the path at a rate of a . I can run through the field at rate b < a . What is area of the region t...
by wwtucker
Fri Apr 07, 2006 6:23 am
Forum: Combinatorics
Topic: Killing in Confusion (probability)
Replies: 3
Views: 3694

Saif wrote:Very close.. but I think you missed the fact that N people JOIN me... so there are N+1 people actually, but that's an easy thing to fix...
True, but it might be easier to reword the question. :)
by wwtucker
Fri Apr 07, 2006 4:26 am
Forum: Combinatorics
Topic: Killing in Confusion (probability)
Replies: 3
Views: 3694

Assertion: For 3 people (n people), the order of the killing is determined by selecting a permutation of the set {1,2,3} ({1,2,...n}). All permutations have the same probability, 1/P(3) (1/P(n)). Of course, some of these permutations are equivalent in that nobody gets killed after the shooter kills ...
by wwtucker
Thu Apr 06, 2006 12:34 am
Forum: Number
Topic: How Likely To Divide?
Replies: 12
Views: 9304

Assuming a suitable definition of "randomly chosen positive integers":


1/5*(1+1/2+1/9+1/4+9/25)=1999/4500
[tt]
1 2 3 4 5
0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1
2 1 2 0 2 4
3 1 3 4
4 1
[/tt]

EDIT: changed 1819 to 1999
by wwtucker
Wed Apr 05, 2006 4:50 pm
Forum: Combinatorics
Topic: How many strings can we construct
Replies: 12
Views: 7736

I should note that the correct use of this formula is, as you might suspect, pCq=p!/(q!*(p-q)!). The use of nCr as a function with two arguments is an abuse of the notation (but one that is easy to write out without formatting).
by wwtucker
Wed Apr 05, 2006 9:25 am
Forum: Combinatorics
Topic: How many strings can we construct
Replies: 12
Views: 7736

Chimerade wrote:Could you tell me what nCr stands for ?
nCr (nCr now that we have subscripts) is just the number of combinations:
nCr(p,q)=p!/(q!*(p-q)!).
(Our answers agree.)
by wwtucker
Wed Apr 05, 2006 12:38 am
Forum: Combinatorics
Topic: No Ones
Replies: 1
Views: 2441

First guess:

for n, r=(9/10)^n
(9/10)^n<p -> n*ln(.9)<ln(p) -> n>ln(p)/ln(.9)

This should be true for no 1's, no 2's, no 3's.
No 0's is quite a bit more complicated.
by wwtucker
Sat Apr 01, 2006 11:38 am
Forum: Combinatorics
Topic: How many strings can we construct
Replies: 12
Views: 7736

I get 2*nCr(16,8)*nCr(15,8)...
by wwtucker
Thu Mar 30, 2006 7:49 pm
Forum: Recreational
Topic: Missing Wedding Ring Finger
Replies: 17
Views: 13415

Now I get it - you already had the classic answer. That makes a lot more sense. Possible alternative answer:

The Police did not act because they (effectively) broke up sometime in the mid-80's.