Search found 53 matches

by uws8505
Thu Apr 22, 2010 3:44 pm
Forum: Number Theory
Topic: Nonzero Factoring
Replies: 0
Views: 1410

Nonzero Factoring

How many natural numbers not exceeding N can be expressed as a product of two numbers a and b, not necessarily distinct, which are not 1 and has no zeros as their digits? How about numbers of the property with additional constraint that 0 should be one of the digits? Example: 10000 has four zeros as...
by uws8505
Fri Apr 16, 2010 6:24 pm
Forum: Geometry
Topic: Constructible Numbers
Replies: 3
Views: 4042

Re: Constructible Numbers

Pi cannot be in the expanded group because it is a transcendental number, not an algebraic number (which means it cannot be a solution of a polynomial equation with rational coefficients).

Maybe marked edge can allow all algebraic numbers?
by uws8505
Sat Apr 03, 2010 10:16 am
Forum: Number
Topic: Product and Sum
Replies: 2
Views: 2000

Re: Product and Sum

Possible approach: a * b * c * d = 10a + b a + b + c + d = 10c + d Since 10a + b is multiple of a, b is also multiple of a. a + b + c + d = 10c + d gives a + b = 9c. The only possible values for c are 1 and 2, but if c = 2, then a = b = 9 and it is impossible. (99 = 9 * 11) So c = 1, a + b = 9. b is...
by uws8505
Fri Feb 05, 2010 7:03 pm
Forum: Geometry
Topic: Number of ways to unwrap a polyhedra
Replies: 1
Views: 2650

Re: Number of ways to unwrap a polyhedra

For the cubes(11 total, 4 whose faces are joined to <=2 other faces)
XXX  XX0  XX0  XX0  0X0  0X0  X00  X00  X00  X00
0X0  0XX  0X0  0X0  XX0  XXX  XXX  XX0  XX0  XX0
0X0  0X0  0XX  0X0  0XX  0X0  0X0  0XX  0X0  0XX
0X0  0X0  0X0  0XX  0X0  0X0  0X0  0X0  0XX  00X

XXX00
00XXX
by uws8505
Wed Jan 20, 2010 2:09 pm
Forum: News, Suggestions, and FAQ
Topic: [ code ] tag in solution forums
Replies: 2
Views: 849

Re: [ code ] tag in solution forums

The code tag automatically includes the programming language if you select your language for your account.
(at least I think :) )
by uws8505
Fri Jan 08, 2010 5:39 pm
Forum: Discrete Mathematics
Topic: Domino Tilings in 3d
Replies: 3
Views: 2311

Re: Domino Tilings in 3d

Of course we can define our 3D version of dominos:
shapes formed by the union of two unit cubes meeting face-to-face.

Nevertheless, it seems quite hard to even find the formula for 2*m*n?
by uws8505
Fri Jan 01, 2010 3:29 am
Forum: Game Theory
Topic: Towers of Hanoi Variation
Replies: 5
Views: 4276

Re: Towers of Hanoi Variation

I doubt that it is possible, but think of this: Move the top(smallest) triangle to the middle. Then move the top square to the middle. Repeat the process until you have only one square left on the right and nothing on the left. Move the biggest square to the left. Then move all pieces on the middle ...
by uws8505
Thu Apr 30, 2009 2:43 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 017
Replies: 83
Views: 19669

Re: Problem 017

stupidgeek wrote:three (5) + hundred (7) + and (3) + forty (5) + two (3) = (21)
Your calculation is wrong : 5 + 7 + 3 + 5 + 3 = (7+3) + (5+5) + 3 = 23. So the problem statement is right.
by uws8505
Mon Apr 20, 2009 1:00 am
Forum: Number
Topic: Other Sequences in the Fibonacci Sequence
Replies: 7
Views: 2916

Re: Other Sequences in the Fibonacci Sequence

General formula: F n+k = L k F n + (-1) k+1 F n-k where L n is Lucas number defined by L 1 = 1, L 2 = 3, L n+2 = L n+1 + L n Proof: Induction step only :) F n+k+1 = F n+k + F n+k-1 = L k F n + (-1) k+1 F n-k + L k-1 F n + (-1) k F n-k+1 = (L k + L k-1 ) F n + (-1) k (F n-k+1 - F n-k ) = L k+1 F n + ...
by uws8505
Mon Apr 20, 2009 12:36 am
Forum: Number
Topic: Other Sequences in the Fibonacci Sequence
Replies: 7
Views: 2916

Re: Other Sequences in the Fibonacci Sequence

F n+3 = F n+2 + F n+1 = 2 F n+1 + F n = 3 F n + 2 F n-1 = 3 F n + F n-1 + F n-2 + F n-3 = 4 F n + F n-3 F n+4 = F n+3 + F n+2 = 2 F n+2 + F n+1 = 3 F n+1 + 2 F n = 5 F n + 3 F n-1 = 5 F n + 3 F n-2 + 3 F n-3 = 5 F n + 6 F n-3 + 3 F n-4 = 5 F n + 2 F n-1 - 2 F n-2 + 4 F n-3 + 3 F n-4 = 7 F n - 4 F n-...
by uws8505
Mon Mar 16, 2009 6:43 am
Forum: Game Theory
Topic: 10 Percent Fight
Replies: 1
Views: 2926

10 Percent Fight

In the game of Ten Percent Fight, you control players A, B, and C and the computer (CPU, or whatever) controls players X, Y, and Z. At your turn, for each of your player, you can decide which opponent player to attack. For example, you can choose all A, B, C to attack X, or A to X, B to Y, and C to ...
by uws8505
Fri Feb 13, 2009 12:31 pm
Forum: Recreational
Topic: Five New Fort
Replies: 3
Views: 1094

Re: Five New Fort

How about this one?

prime + prime + prime = number
(Goldbach's Conjecture)
Actually I found a solution two years ago, but I lost it :(
by uws8505
Sat Feb 07, 2009 4:31 am
Forum: News, Suggestions, and FAQ
Topic: Public user statistics
Replies: 7
Views: 2186

Re: Public user statistics

While a good idea, I'm afraid you will see this message soon:
hk wrote:Currently we are not able to handle any functional requests that imply changing the functioning of the website or this forum.
Sorry.
by uws8505
Fri Feb 06, 2009 10:53 am
Forum: News, Suggestions, and FAQ
Topic: is "up to" the same as "less than" or "not greater"
Replies: 8
Views: 1787

"up to" is the same as "not greater than"

I'm not a native speaker, but I thought "up to" as "not greater than" and got a correct answer.
by uws8505
Thu Feb 05, 2009 5:10 pm
Forum: Programming languages
Topic: C++, computing with huge numbers and booleans.
Replies: 21
Views: 7587

Measuring timing in C++

I use both C++ and Mathematica for solving PE problems.
In Mathematica, there are several methods to measure elapsed time, using Timing[] function or package Utilities-ShowTime.
But I do not know anything about timing in C++.
Can someone teach me how to do such a thing in C++?
by uws8505
Thu Jan 29, 2009 1:19 pm
Forum: Discrete Mathematics
Topic: Determinant
Replies: 4
Views: 2367

Determinant

Let a1,a2,...,a100 be random integers between -10 and 10, inclusive. What is the probability of getting zero as the determinant of ┌a1 a2 a3 a4 ... a10 ┐ │a11 a12 a13 a14 ... a20 │ │a21 a22 a23 a24 ... a30 │ │... ... ... ... ... ... │ └a91 a92 a93 a94 ... a100┘ p.s. is there any efficient algorithm ...
by uws8505
Wed Jan 28, 2009 12:31 pm
Forum: Game Theory
Topic: Rolling Dice Continued (#205 modified)
Replies: 1
Views: 1692

Re: Rolling Dice Continued (#205 modified)

I think it would not be so difficult if you know the probability of each case : player 1 wins / player 2 wins / two players draw after a round. Probability(player 1 wins) = p1 Probability(player 2 wins) = p2 Probability(draw) = p3 Then the result will be in the form of infinite series(which can be c...
by uws8505
Sat Jan 17, 2009 11:30 pm
Forum: Game Theory
Topic: A Convulted Chess Positioning
Replies: 4
Views: 3380

Re: A Convulted Chess Positioning

Do you mean
8 pawns, 2 rooks, 2 bishops, 2 knights, 1 queen and 1 king
or two sets of the above(black and white)?

Anyway, it is easily seen that it is impossible to defend an attack by a knight because it can jump over others. But I can't see anything else :?
by uws8505
Thu Jan 01, 2009 7:35 am
Forum: Number Theory
Topic: Diophantine Equations
Replies: 11
Views: 4072

Re: Diophantine Equations

elendiastarman wrote:#3:
...
Again, almost all resulting 4-tuples (x,y,z,n) have at least one prime, the first exception is (1,39,40,59). How many such prime-free 4-tuples are there where 0<x<=y<=z<=n<=1,000,000?
I think you missed that 59 is a prime. Or are you considering only primality of x, y, z but not n?
by uws8505
Tue Dec 09, 2008 4:13 am
Forum: Clarifications on Project Euler Problems
Topic: Problem 200
Replies: 23
Views: 5204

Problem 200

Is there any odd prime-proof sqube which contains the contiguous sub-string "200"?