Just how good are you at Math?

Just how good are you at Math?

Richard Phipps

Have a go if you like this kind of thing..
http://www.gocomics.com/foxtrot/2006/10/15/

Don't cheat!

Simon Parzer

So what? It's just a Sudoku.

FMC

Quote:

So what? It's just a Sudoku.

I'm too intelligent... MUAHAHHAH

Richard Phipps

Simon: Did you see those math equations? Solve them! ::)

HoHo

There was only one equasion I couldn't do without aid, the one in the end of second row. I'm not that good with integrals and it was long time ago when I last used them :-/

Inphernic

Quote:

Did you see those math equations? Solve them!

Are you trying to suggest that those are somehow "teh complicated maths"?

Richard Phipps

No. Just giving a slight mental workout.

Bruce Perry

Maths, not math. Stand up for your country and its language!

Richard Phipps

There's not many of us Brits here.. :'(

Thomas Harte

Quote:

There's not many of us Brits here..

And at least one of us has to call it "math" for their day job anyway! Damn the American market we're trying to break.

Goalie Ca

Well.. that soduku actually appears to be valid.. (foxtrox never lies!) not gonna solve it. Anyone have code?

Inphernic

http://www.duckiehorde.net/div0d.gif

Evert

Quote:

Just how good are you at Math?

Too good to spend more than a minute or so with that puzzle.
The other day I read the preselection test for the National Dutch Arithmetic Test in the news paper (apparently, school teachers these days are worse at arithmetic than their students are). It took me five minutes to do the problems in there in my head correctly. I decided that I wasn't the target audience.

Jakub Wasilewski

Quote:

The other day I read the preselection test for the National Dutch Arithmetic Test in the news paper (apparently, school teachers these days are worse atarithmetic than their students are). It took me five minutes to do the problems in there in my head correctly. I decided that I wasn't the target audience.

You are going for a PhD in Physics. You are definitely not in the "average" cross-section of society when it comes to Math, what did you expect.

That being said, there are no actual problems there. All the formulas are very simple, most of them can be calculated without even starting up the math co-processor in your brain . It's just a matter of training in reading the notation, I think.

Evert

Quote:

what did you expect

I expected to be able to do the test in a few minutes correctly in my head.

ImLeftFooted

#SelectExpand
   1#ifndef SUDOKU_H
   2#define SUDOKU_H
   3
   4// Represents a 9x9 Sudoku board with methods for solving it
   5class Sudoku {
   6public:
  
  typedef int Board[9][9];
  
  // Copies board to the class's internal memory
  void submit(const Board &board);
  
  // Solves the Sudoku board stored in the class, storing
  // the final board in solution.  Returns true if a
  // solution was found or false if one could not be found.
  bool solve(Board &solution);
  
  18private:
  
  // Returns the discovered numbers found in the cell's row, column, and box.
  // Note cell's value will not be included in the result.
  //
  // 'where' specifies where to look where 0 means the cell's row, 1 means
  // the cell's column and 2 means the cell's box.
  // 'cell' must be a pointer to an element in the 'board' array.
  // Set completeOnly to false to get all bits owned by friends instead of
  // only completed numbers.
  // 
  // To check if 3 is a friend of cell, you would shift the return value right
  // 2 and bitwise AND it with 1.
  // To check if 5 is a friend of cell, you would shift the return value right
  // 4 and bitwise AND it with 1.
  // And so on until 9.
  int getFriends(int where, int *cell, bool completeOnly = true);
  
  Board board;
  37};
  38
  39#endif
  40
  41using namespace std;
  42
  43void Sudoku::submit(const Board &from)
  44{
  /* First off, we set bits to represent the possible values
   * each box on the board can have.  1 represents 1, 1 << 1
   * represents 2, 1 << 2 represents 3 and so on.
   * We set this bits while copying to the board array.
   */
  
  for(int i = 0; i < 81; i++) {
      
      if(!from[0]<i>)
          board[0]<i> = 0x1ff; // Set all bits 1-9
      else
          board[0]<i> = (1 << (from[0]<i> - 1));
  }
  58}
  59
  60bool Sudoku::solve(Board &answer)
  61{
  // So we have two stages.  In the first stage we narrow down the possible
  // numbers for a given cell.  In the second stage we iterate through the
  // cells in a given row/column/box seeing how many can take a given number,
  // if theres only 1 we set that number.
      
  int stage1actions;
  int stage2actions;
  
  do {
      
      stage1actions = 0;
      stage2actions = 0;
      
      // Stage 1 - Here we go through each cell on the board and update the
      // cells list of possible numbers (in other words, further restrict
      // the numbers a cell is allowed to be).
      
      bool didChange = true;
      
      do {
          didChange = false;
          
          for(int j = 0; j < 81; j++) {
              
              int original = board[0][j];
              
              board[0][j] &= ~getFriends(0, board[0] + j)
                          &  ~getFriends(1, board[0] + j)
                          &  ~getFriends(2, board[0] + j);
              
              if(board[0][j] != original) {
                  
                  stage1actions++;
                  didChange = true;
              }
          }
          
      } while(didChange);
      
      // Stage 2 - Now we go through each cell on the board and check to see
      // if the row/column/box its in has any numbers that only the cell could
      // be.  If this is the case we set the cell to that number.
      
      // loop all cells
      for(int j = 0; j < 81; j++) {
          
          int bitsSet = 0;
          
          for(int p = 8; p >= 0; p--) {
              
              if((board[0][j] >> p) & 1)
                  bitsSet++;
          }
          
          if(bitsSet == 0) {
              
              // Shit a cell is bad!
              continue;
          }
          
          if(bitsSet == 1) {
              
              // This cell is a complete number.
              continue;
          }
          
          int bits = getFriends(0, board[0] + j, false)
                   & getFriends(1, board[0] + j, false)
                   & getFriends(2, board[0] + j, false);
          
          for(int l = 8; l >= 0; l--) {
              
              // If no friends have this bit set yet we do..
              if(!((bits >> l) & 1) && ((board[0][j] >> l) & 1)) {
                  
                  board[0][j] = (1 << l);
                  stage2actions++;
                  
                  break;
              }
          }
      }
      
  } while(stage1actions || stage2actions);
  
  bool ret = true;
  
  for(int i = 0; i < 81; i++) {
      
      int &cell = board[0]<i>;
      int &dest = answer[0]<i>;
      
      if(!cell) {
          
          ret = false;
          
          continue;
      }
      
      // Check to see if this cell has more then one bit set and set dest at
      // the same time.
      bool bitFound = 0;
      for(int l = 8; l >= 0; l--) {
          
          if((cell >> l) & 1) {
              
              if(bitFound) {
                  
                  dest = 0;
                  ret = false;
              }
              else
                  dest = l + 1;
              
              bitFound = true;
          }
      }
  }
  
  return ret;
 182}
 183
 184int Sudoku::getFriends(int where, int *cell, bool completeOnly)
 185{
  int ret = 0;
  
  switch(where) {
      case 0:
      {
          int *row = board[(cell - board[0]) / 9];
          
          // Loop through all elements in the row
          for(int i = 0; i < 9; i++) {
              
              if(row + i == cell)
                  continue;
              
              int bit = 0;
              
              // Loop through all bits in cell
              for(int j = 0; j < 9; j++) {
                  
                  if((row<i> >> j) & 1) {
                      
                      if(bit && completeOnly) {
                          
                          bit = 0;
                          break;
                      }
                      
                      bit |= 1 << j;
                  }
              }
              
              ret |= bit;
          }
          
          break;
      }
      case 1:
      {
          int *col = &board[0][(cell - board[0]) % 9];
          
          // Loop through all elements in the column
          for(int i = 0; i < 9; i++) {
              
              if(col + i * 9 == cell)
                  continue;
              
              int bit = 0;
              
              // Loop through all bits in cell
              for(int j = 0; j < 9; j++) {
                  
                  if((col[i * 9] >> j) & 1) {
                      
                      if(bit && completeOnly) {
                          
                          bit = 0;
                          break;
                      }
                      
                      bit |= 1 << j;
                  }
              }
              
              ret |= bit;
          }
          
          break;
      }
      case 2:
      {
          // Algorithm to find the upper left corner of the box cell is located in
          int *box = &board[0][((cell - board[0]) % 9) / 3 * 3 + (cell - board[0]) / 9 / 3 * 27];
          
          int bit;
          
          // Loop through all elements in the box
          for(int i = 0; i < 21; i++) {
              
              if(box + i == cell)
                  goto Cont;
              
              bit = 0;
              
              // Loop through all bits in cell
              for(int j = 0; j < 9; j++) {
                  
                  if((box<i> >> j) & 1) {
                      
                      if(bit && completeOnly) {
                          
                          bit = 0;
                          break;
                      }
                      
                      bit |= 1 << j;
                  }
              }
              
              ret |= bit;
              
              // 'continues' the loop
              Cont:;
              
              // If we're on the edge of the box jump ahead to the next row
              if(i == 2 || i == 11)
                  i += 6;
          }
          
          break;
      }
  }
  
  return ret;
 298}
 299
 300
 301#include <iostream>
 302#include <iomanip>
 303
 304#ifdef WIN32
 305#include <windows.h>
 306#endif
 307using namespace std;
 308
 309int main()
 310{
  /* Medium level board *solved* */
  /*
  int board[9][9] =
  {
      { 0, 6, 0, 1, 0, 4, 0, 5, 0 },
      { 0, 0, 8, 3, 0, 5, 6, 0, 0 },
      { 2, 0, 0, 0, 0, 0, 0, 0, 1 },
      { 8, 0, 0, 4, 0, 7, 0, 0, 6 },
      { 0, 0, 6, 0, 0, 0, 3, 0, 0 },
      { 7, 0, 0, 9, 0, 1, 0, 0, 4 },
      { 5, 0, 0, 0, 0, 0, 0, 0, 2 },
      { 0, 0, 7, 2, 0, 6, 9, 0, 0 },
      { 0, 4, 0, 5, 0, 8, 0, 7, 0 }
  };
  */
  
  /* Hard level board *solved* */
  int board[9][9] =
  {
      { 0, 9, 1, 0, 0, 0, 8, 0, 0 },
      { 0, 0, 0, 2, 0, 0, 3, 0, 0 },
      { 2, 0, 5, 1, 0, 6, 9, 0, 0 },
      { 1, 0, 0, 0, 0, 0, 5, 0, 0 },
      { 0, 3, 0, 0, 5, 0, 0, 2, 0 },
      { 0, 0, 4, 0, 0, 0, 0, 0, 9 },
      { 0, 0, 3, 5, 0, 4, 2, 0, 6 },
      { 0, 0, 6, 0, 0, 8, 0, 0, 0 },
      { 0, 0, 8, 0, 0, 0, 7, 4, 0 }
  };
  
  cout << "Intial board:\n";
  
  cout << "-------------------------\n| ";
  
  for(int i = 0; i < sizeof(board) / sizeof(board[0][0]); i++)
      cout << board[0]<i>
           << ((i + 1) % 9 ? ((i + 1) % 3 ? " " : " | ") : ((i + 1) % 27 ? " |\n| " : " |\n| --------------------- |\n| "));
  
  Sudoku sudoku;
  
 351#ifdef WIN32
  time_t start = GetTickCount();
 353#endif
  
  sudoku.submit(board);
  if(sudoku.solve(board))
      cout << "Board solved!\n";
  else
      cout << "Board unsolvable.\n";
  
 361#ifdef WIN32
  time_t t = GetTickCount() - start;
  
  cout << "Milliseconds to solve: " << t << endl;
 365#endif
  
  cout << "Final board:\n";
  
  cout << "-------------------------\n| ";
  
  for(int i = 0; i < sizeof(board) / sizeof(board[0][0]); i++)
      cout << board[0]<i>
           << ((i + 1) % 9 ? ((i + 1) % 3 ? " " : " | ") : ((i + 1) % 27 ? " |\n| " : " |\n| --------------------- |\n| "));
  
  system("PAUSE");
  
  return 0;
 378}

Ok, now let me run it. I'll do an edit once I have the results.

[edit]
It couldnt get it. Does someone want to double check my input board?

#SelectExpand
  1Intial board:
  2-------------------------
0 7 3 | 0 9 0 | 0 4 0 |
9 0 0 | 4 0 3 | 0 0 7 |
0 0 0 | 6 0 0 | 0 0 8 |
--------------------- |
0 4 0 | 0 0 0 | 3 6 0 |
7 0 0 | 0 0 0 | 0 0 1 |
0 2 9 | 0 0 0 | 0 5 0 |
--------------------- |
5 0 0 | 0 0 1 | 0 0 0 |
0 0 6 | 0 0 8 | 0 0 3 |
0 3 0 | 0 4 0 | 1 7 0 |
--------------------- |
Board unsolvable.
 16Milliseconds to solve: 10
 17Final board:
 18-------------------------
6 7 3 | 8 9 2 | 0 4 5 |
9 8 2 | 4 5 3 | 6 1 7 |
1 5 4 | 6 7 0 | 9 3 8 |
--------------------- |
8 4 1 | 7 2 5 | 3 6 9 |
7 6 5 | 9 3 4 | 8 2 1 |
3 2 9 | 1 8 6 | 7 5 4 |
--------------------- |
5 9 7 | 3 6 1 | 4 8 2 |
4 1 6 | 2 0 8 | 5 9 3 |
2 3 8 | 5 4 9 | 1 7 6 |
--------------------- |
Press any key to continue . . .

nonnus29

Yeah, I'm not so great at math (ie I've had to work at it ALOT over the years) but those 'problems' are pretty easy. But he was constrained by the size of the squares. It's not like he has room for something interesting like:

$<math>\frac{dx}{dt} = \frac{1}{t}x + \sqrt{x}</math>$

8-)

Don't ask me for the solution; it's been awhile since diff eq....

Goalie Ca

It appears you missed one 7 (the hex subtraction, i assumed it was 8 instead of B). And there is a six right to the left of that 7 which shouldn't be there. That 6 should be 2 squares to the left.

Here's what i got...

-------------------------
| 0 7 3 | 0 9 0 | 0 4 0 |
| 9 0 0 | 4 0 3 | 0 0 7 |
| 0 0 0 | 6 0 0 | 0 0 8 |
| --------------------- |
| 0 4 0 | 0 0 0 | 3 6 0 |
| 7 0 0 | 0 0 0 | 0 0 1 |
| 0 2 9 | 0 0 0 | 0 5 0 |
| --------------------- |
| 5 0 0 | 0 0 1 | 0 0 0 |
| 6 0 0 | 7 0 8 | 0 0 3 |
| 0 3 0 | 0 4 0 | 1 7 0 |
| --------------------- |

edit: i remember there being a foxtrot a while back which was written in code... maybe ascii or rot13 or something... but it actually did translate

ImLeftFooted

Looks like its a real sudoku board

1Intial board:
2-------------------------
0 7 3 | 0 9 0 | 0 4 0 |
9 0 0 | 4 0 3 | 0 0 7 |
0 0 0 | 6 0 0 | 0 0 8 |
--------------------- |
0 4 0 | 0 0 0 | 3 6 0 |
7 0 0 | 0 0 0 | 0 0 1 |
0 2 9 | 0 0 0 | 0 5 0 |
--------------------- |
5 0 0 | 0 0 1 | 0 0 0 |
6 0 0 | 7 0 8 | 0 0 3 |
0 3 0 | 0 4 0 | 1 7 0 |
--------------------- |
Board solved!
16Milliseconds to solve: 10
17Final board:
18-------------------------
1 7 3 | 8 9 2 | 6 4 5 |
9 8 6 | 4 5 3 | 2 1 7 |
4 5 2 | 6 1 7 | 9 3 8 |
--------------------- |
8 4 1 | 2 7 5 | 3 6 9 |
7 6 5 | 9 3 4 | 8 2 1 |
3 2 9 | 1 8 6 | 7 5 4 |
--------------------- |
5 9 7 | 3 6 1 | 4 8 2 |
6 1 4 | 7 2 8 | 5 9 3 |
2 3 8 | 5 4 9 | 1 7 6 |
--------------------- |
Press any key to continue . . .

Goalie Ca

Sweet

Ron Ofir

Hehe, nice. And nice app you got there, Dustin!

BTW, did anyone notice something weird with inphernic's image?
(How do you link to attached images anyway?)

EDIT: Whoa! Now I can't even click it! Seems like ML's cool DHTML thingies are a bit bogus.

MiquelFire

Resizing in GD does that.

And what browser are you using?

ImLeftFooted

Quote:

And nice app you got there, Dustin!

Thanks

Quote:

(How do you link to attached images anyway?)

In the attachments tab, after the file finishes transfering, you right click the link and go copy link location.

Then you make an [img href] tag where href is the link locatin you copied from the link and then pasted, like so:
{"name":"590325","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/d\/1\/d181a533028799bb5827d1990fa7586d.png","w":561,"h":271,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/d\/1\/d181a533028799bb5827d1990fa7586d"}

Johan Halmén

Is that an image you have there, Dustin? My browser only shows ndef.

ImLeftFooted

Weird, everythings going to shit.

http://www.allegro.cc/images/rcache/d181a533028799bb5827d1990fa7586d.png is the image, which was attached to this post:
http://www.allegro.cc/files/download-attachment/?area=forum%20post&id=620779

Thread #588050. Printed from Allegro.cc