Search found 38 matches

by rmillika
Thu Nov 10, 2011 2:12 pm
Forum: News, Suggestions, and FAQ
Topic: Recent Article And Website Problems
Replies: 4
Views: 3508

Re: Recent Article And Website Problems

I have been unable to log in for a while. It is asking for an activation code and offers to send one to my e-mail address, but the code never comes through. It has the right e-mail for me, and I have checked my spam box as well.
by rmillika
Wed Nov 10, 2010 12:29 am
Forum: Number
Topic: problem 17
Replies: 1
Views: 2739

Re: problem 17

There is a separate forum specifically for discussing the problems. So please post your queries there. However, it asks that you not post code as it may give the problem away.
by rmillika
Wed Sep 22, 2010 4:39 pm
Forum: Recreational
Topic: permutations
Replies: 6
Views: 4003

Re: permutations

As addition and multiplication are commutative and associative, the permutations don't matter. It is just the collection of digits in each number. I found these two by hand by looking for pairs of digits that have the same product, then combining them to produce the same sum. So 2*3=1*6 but 2+3 is 2...
by rmillika
Mon Sep 20, 2010 10:35 pm
Forum: Recreational
Topic: permutations
Replies: 6
Views: 4003

Re: permutations

How about 232319 and 161633?
by rmillika
Mon Aug 16, 2010 6:55 pm
Forum: Resources
Topic: Paper/Pencil Problems
Replies: 71
Views: 75123

Re: Paper/Pencil Problems

Problem 158 yields an algebraic answer to pencil and paper, though calculating the final answer takes a high-precision calculator
by rmillika
Mon Aug 02, 2010 10:38 pm
Forum: Applied Mathematics
Topic: Velocity of object with inverse square force?
Replies: 1
Views: 7799

Re: Velocity of object with inverse square force?

If object_1 is acted on by a force from object_2 that is inversely proportional to the square of the objects distance (think gravity), is there away to determine the velocity of object_1 at a given distance from object_2? So the force between the two things is: F=-1/r^2 where r is the distance betw...
by rmillika
Tue Jul 20, 2010 7:03 pm
Forum: Number
Topic: HAKMEM Item 39
Replies: 4
Views: 4105

Re: HAKMEM Item 39

I strongly suspect that one can make an infinite string with three characters. This would answer both questions. An approach, which I have not fully proved, is provided by the rules: start with 0. Each step, take the existing string and replace 0 with 02, 1 with 012, and 2 with 010212. So we have a ...
by rmillika
Wed Jul 07, 2010 10:33 pm
Forum: Combinatorics
Topic: Vending machine
Replies: 10
Views: 8116

Re: Vending machine

That would be a better strategy than what I had in mind, so I am very interested to hear it! The best I could achieve with my simple strategy was P(1000,5)=333: Identify 9 products with every 3 parcels we buy, as follows: Calling the nine products a,b,c,d,e,f,g,h and i, we buy the parcels addgh, be...
by rmillika
Fri Jul 02, 2010 12:25 am
Forum: Recreational
Topic: Nice set theory exercise
Replies: 20
Views: 9578

Re: Nice set theory exercise

How about all numbers of the form sqrt(p1*p2*p3*...) for the p's distinct primes? It is certainly explicit and uncountable. I think if you find a set that is linearly dependent over Q then you can prove some sqrt(product of primes) to be rational This set is countable. There's a one-to-one mapping ...
by rmillika
Wed Jun 30, 2010 4:46 pm
Forum: Recreational
Topic: Nice set theory exercise
Replies: 20
Views: 9578

Re: Nice set theory exercise

How about all numbers of the form sqrt(p1*p2*p3*...) for the p's distinct primes? It is certainly explicit and uncountable. I think if you find a set that is linearly dependent over Q then you can prove some sqrt(product of primes) to be rational
by rmillika
Wed Jun 09, 2010 6:39 pm
Forum: Clarifications on Project Euler Problems
Topic: Problem 274
Replies: 11
Views: 3979

Re: Problem 274

That is all primes except 2 and 5.
by rmillika
Tue Nov 24, 2009 5:48 pm
Forum: Combinatorics
Topic: Gambling
Replies: 4
Views: 5272

Re: Gambling

The proofs are not difficult: For the first part, in a fair game the expected value to A cannot change. As his only outcomes are 0 and A+B, his probability of A+B must be a/(A+B) http://en.wikipedia.org/wiki/Gambler%27s_ruin has the result for an unfair coin with an indication of how to get it For t...
by rmillika
Wed Oct 28, 2009 10:48 pm
Forum: Number Theory
Topic: Maximum Time to Reach a Happy Loop
Replies: 9
Views: 5458

Re: Maximum Time to Reach a Happy Loop

So accepting that maxindx13=1.127 x 10200-1, maxindx14 will end with 1.4 x 10198 9s. But as your example shows, the number can be a thousand times larger than this. And the sum of digits of maxindx15 will be about 1/9 the actual value of maxindx14, so of order 10^(10198)
by rmillika
Tue Oct 20, 2009 9:56 am
Forum: Game Theory
Topic: Towers of Hanoi Variation
Replies: 5
Views: 11297

Re: Towers of Hanoi Variation

In that case, I think the easiest is to move the squares to the center peg, the triangles to the left, and the squares to the right, using the standard solution. You have to clear the largest square from the left peg, and putting it on the triangles is in the way. So for four of each we need 3*(2^4-...
by rmillika
Sat Oct 17, 2009 1:00 am
Forum: Game Theory
Topic: Towers of Hanoi Variation
Replies: 5
Views: 11297

Re: Towers of Hanoi Variation

If the rule is that any square can go on any triangle, we can just view this as a stage of the original game with the number of disks equal to the sum of the squares and triangles. So for 4 squares and 4 triangles we have eight disks with a linear order among them. If we started with all the disks o...
by rmillika
Fri Sep 18, 2009 1:36 am
Forum: Game Theory
Topic: Super Smash Bros. Tourney
Replies: 7
Views: 11961

Re: Super Smash Bros. Tourney

Here is the start of the sheet. Based on the preview, you will have to work on the spacing. The column headings should be clear, and the powers of 2 are the sum of the various Qty columns. Qty 1 is the average number of each level at round 1 = 64/9. Pwin1 is the probability that a character of that ...
by rmillika
Tue Sep 15, 2009 5:04 pm
Forum: Game Theory
Topic: Super Smash Bros. Tourney
Replies: 7
Views: 11961

Re: Super Smash Bros. Tourney

My complete results are 1 wins 0.000104453, 2 wins 0.002418018, 3 wins 0.012064299, 4 wins 0.033487702, 5 wins 0.068734128, 6 wins 0.117823111, 7 wins 0.179552404, 8 wins 0.252146623, 9 wins 0.333669262. Note that the 8 probability is within 1/3 of a single win of yours. I think these agree pretty w...
by rmillika
Mon Sep 14, 2009 4:49 pm
Forum: Game Theory
Topic: Super Smash Bros. Tourney
Replies: 7
Views: 11961

Re: Super Smash Bros. Tourney

I make it 0.333669262 that a level 9 will win and 0.000104453 that a level 1 will win. This was done in Excel so there will be rounding error. The sheet played each level against an even mix of levels to calculate the winning chance on the first round. For each round after that, it took the level di...
by rmillika
Tue Aug 25, 2009 12:23 am
Forum: Geometry
Topic: Reverse-engineering Voronoi Diagrams
Replies: 7
Views: 9836

Re: Reverse-engineering Voronoi Diagrams

A good example. You are right that things are more subtle than I thought.
by rmillika
Mon Aug 17, 2009 9:04 pm
Forum: Geometry
Topic: Reverse-engineering Voronoi Diagrams
Replies: 7
Views: 9836

Re: Reverse-engineering Voronoi Diagrams

If the cells are more complicated and irregular, you may be able to derive the points (I'm not sure how to interpret rmillika 's algorithm, I think it's more complicated than stated). I don't think so for any of the bounded regions. Each bounded region is a convex polygon where each side is a porti...