## Search found 53 matches

- Thu Apr 22, 2010 3:44 pm
- Forum: Number Theory
- Topic: Nonzero Factoring
- Replies:
**0** - Views:
**1310**

### 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...

- Fri Apr 16, 2010 6:24 pm
- Forum: Geometry
- Topic: Constructible Numbers
- Replies:
**3** - Views:
**3243**

### 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?

Maybe marked edge can allow all algebraic numbers?

- Sat Apr 03, 2010 10:16 am
- Forum: Number
- Topic: Product and Sum
- Replies:
**2** - Views:
**1896**

### 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...

- Fri Feb 05, 2010 7:03 pm
- Forum: Geometry
- Topic: Number of ways to unwrap a polyhedra
- Replies:
**1** - Views:
**1918**

### 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

- Wed Jan 20, 2010 2:09 pm
- Forum: News, Suggestions, and FAQ
- Topic: [ code ] tag in solution forums
- Replies:
**2** - Views:
**825**

### 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 )

(at least I think )

- Fri Jan 08, 2010 5:39 pm
- Forum: Discrete Mathematics
- Topic: Domino Tilings in 3d
- Replies:
**3** - Views:
**2188**

### Re: Domino Tilings in 3d

Of course we can define our 3D version of dominos:

shapes formed by the union of two unit

Nevertheless, it seems quite hard to even find the formula for 2*m*n?

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?

- Fri Jan 01, 2010 3:29 am
- Forum: Game Theory
- Topic: Towers of Hanoi Variation
- Replies:
**5** - Views:
**3476**

### 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 ...

- Thu Apr 30, 2009 2:43 am
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 017
- Replies:
**83** - Views:
**19021**

### Re: Problem 017

Your calculation is wrong : 5 + 7 + 3 + 5 + 3 = (7+3) + (5+5) + 3 = 23. So the problem statement is right.stupidgeek wrote:three (5) + hundred (7) + and (3) + forty (5) + two (3) = (21)

- Mon Apr 20, 2009 1:00 am
- Forum: Number
- Topic: Other Sequences in the Fibonacci Sequence
- Replies:
**7** - Views:
**2815**

### 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 + ...

- Mon Apr 20, 2009 12:36 am
- Forum: Number
- Topic: Other Sequences in the Fibonacci Sequence
- Replies:
**7** - Views:
**2815**

### 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-...

- Mon Mar 16, 2009 6:43 am
- Forum: Game Theory
- Topic: 10 Percent Fight
- Replies:
**1** - Views:
**2170**

### 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 ...

- Fri Feb 13, 2009 12:31 pm
- Forum: Recreational
- Topic: Five New Fort
- Replies:
**3** - Views:
**1063**

### 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

prime + prime + prime = number

(Goldbach's Conjecture)

Actually I found a solution two years ago, but I lost it

- Sat Feb 07, 2009 4:31 am
- Forum: News, Suggestions, and FAQ
- Topic: Public user statistics
- Replies:
**7** - Views:
**2129**

### 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.

- 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:
**1688**

### "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.

- Thu Feb 05, 2009 5:10 pm
- Forum: Programming languages
- Topic: C++, computing with huge numbers and booleans.
- Replies:
**21** - Views:
**7397**

### 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++?

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++?

- Thu Jan 29, 2009 1:19 pm
- Forum: Discrete Mathematics
- Topic: Determinant
- Replies:
**4** - Views:
**2241**

### 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 ...

- Wed Jan 28, 2009 12:31 pm
- Forum: Game Theory
- Topic: Rolling Dice Continued (#205 modified)
- Replies:
**1** - Views:
**1612**

### 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...

- Sat Jan 17, 2009 11:30 pm
- Forum: Game Theory
- Topic: A Convulted Chess Positioning
- Replies:
**4** - Views:
**2654**

### 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

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

- Thu Jan 01, 2009 7:35 am
- Forum: Number Theory
- Topic: Diophantine Equations
- Replies:
**11** - Views:
**3965**

### Re: Diophantine Equations

I think you missed that 59 is a prime. Or are you considering only primality of x, y, z but not n?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?

- Tue Dec 09, 2008 4:13 am
- Forum: Clarifications on Project Euler Problems
- Topic: Problem 200
- Replies:
**23** - Views:
**4938**

### Problem 200

Is there any

**odd**prime-proof sqube which contains the contiguous sub-string "200"?