Your Mission is to find the best score for the pattern 

     a  b  c
     d  e  f
     g  h  i     where a to i stand for one of 1 2 3 4 5 6 7 8 9 uniquely !

for example    1  2  3
                        4  5  6
                        7  8  9

The Pattern Score is calculated as :

 =  Rows–Row Products+Columns–Column Products–Product of Diagonals–Product of Corners–Product of Diamonds 
     
Which means in the example pattern the Score is :
= 123–6+456–120+789–504+147–28+258–80+369–162–45–105–189–384
=519

Find the Pattern for getting the HIGHEST SCORE !

Seems like it should be easy if you just set up the permutations in a spreadsheet and plug in the formula-- maybe I'll play with it later.

In such puzzles I want to run Visual Studio Express C/C++ so it'll do it for me..

Didn't have time for it, so the first attempt 3023.

Spoiler

 

 

 

Edited February 6, 20196 yr by Sensei

Hi Sensei,

Yes, a good answer !

I got 3025 and if you can better it it will be interesting !

Is there a Combination for a score more than 3025 ?

A more involved Puzzle will be :

Your Mission is to find the best score for the pattern 

     a  b  c
     d  e  f
     g  h  i     where a to i stand for one of 1 2 3 4 5 6 7 8 9 uniquely !

for example     9  7  5
                        8  4  3
                        6  2  1

The Pattern Score is calculated as :

 =  Rows – Columns + Product of Diagonals – Product of Corners + Product of Ribs – Product of Diamond 
     +  Sum of Corners + Sum of Squares of Diamonds + Cube of the Center Number

Which means in the example pattern the Score is :
= 975+843+621 –986–742–531 + 9*4*1+6*4*5–9*5*1*6 +8*4*3+7*4*2– 8*7*3*2 +9+5+1+6+8^2+7^2+3^2+2^2+4^3
= 93

Find the Pattern for getting the HIGHEST SCORE !

1 hour ago, Commander said:

Yes, a good answer !

I got 3025 and if you can better it it will be interesting !

Is there a Combination for a score more than 3025 ?

There are two mirror answers of 3025:

/*
 * PuzzleTest v1.0 (c) 2019 created by Sensei.
 */
#include <stdio.h>

void decode( int index, int data[ 3 ][ 3 ] )
{
    for( int i = 0; i < 9; i++ )
    {
        int value = index % 10;
        data[ i / 3 ][ i % 3 ] = value;
        index /= 10;
    }
}

bool has_zeroes( const int data[ 3 ][ 3 ] )
{
    for( int j = 0; j < 3; j++ )
    {
        for( int i = 0; i < 3; i++ )
        {
            if( data[ j ][ i ] <= 0 ) return( true );
        }
    }
    return( false );
}

bool has_duplicates( const int data[ 3 ][ 3 ] )
{
    bool result = false;
    int digits[ 10 ] = { 0 };
    for( int j = 0; j < 3; j++ )
    {
        for( int i = 0; i < 3; i++ )
        {
            int value = data[ j ][ i ];
            if( digits[ value ] != false ) return( true ); 
            digits[ value ] = true;
        }
    }
    return( false );
}

int calc_score_column( const int data[ 3 ][ 3 ], int column )
{
    return( data[ 0 ][ column ] * 100 + data[ 1 ][ column ] * 10 + data[ 2 ][ column ] );
}

int calc_score_column_product( const int data[ 3 ][ 3 ], int column )
{
    return( data[ 0 ][ column ] * data[ 1 ][ column ] * data[ 2 ][ column ] );
}

int calc_score_row( const int data[ 3 ][ 3 ], int row )
{
    return( data[ row ][ 0 ] * 100 + data[ row ][ 1 ] * 10 + data[ row ][ 2 ] );
}

int calc_score_row_product( const int data[ 3 ][ 3 ], int row )
{
    return( data[ row ][ 0 ] * data[ row ][ 1 ] * data[ row ][ 2 ] );
}

int calc_score( const int data[ 3 ][ 3 ] )
{
    int score = 0;
    for( int i = 0; i < 3; i++ )
    {
        score += calc_score_column( data, i );
        score -= calc_score_column_product( data, i );
        score += calc_score_row( data, i );
        score -= calc_score_row_product( data, i );
    }
    score -= data[ 0 ][ 0 ] * data[ 1 ][ 1 ] * data[ 2 ][ 2 ];
    score -= data[ 0 ][ 2 ] * data[ 1 ][ 1 ] * data[ 2 ][ 0 ];
    score -= data[ 0 ][ 1 ] * data[ 2 ][ 1 ] * data[ 1 ][ 0 ] * data[ 1 ][ 2 ];
    score -= data[ 0 ][ 0 ] * data[ 0 ][ 2 ] * data[ 2 ][ 0 ] * data[ 2 ][ 2 ];
    return( score );
}

int calc_score( int index )
{
    int data[ 3 ][ 3 ] = { 0 };
    decode( index, data );
    if( has_zeroes( data ) ) return( -1 );
    if( has_duplicates( data ) ) return( -1 );
    return( calc_score( data ) );
}

void show( const int data[ 3 ][ 3 ] )
{
    for( int j = 0; j < 3; j++ )
    {
        for( int i = 0; i < 3; i++ )
        {
            printf( "%d ", data[ j ][ i ] );
        }
        printf( "\n" );
    }
    printf( "\n" );
}

void show( int index )
{
    int data[ 3 ][ 3 ] = { 0 };
    decode( index, data );
    show( data );
}

int main( int argc, int argv[] )
{
#if 0
    int data[ 3 ][ 3 ] =
    {
        { 1, 2, 3 },
        { 4, 5, 6 },
        { 7, 8, 9 },
    };
    show( data );
    printf( "Score is %d", calc_score( data ) );
#endif
#if 0
    int data[ 3 ][ 3 ] =
    {
        { 9, 8, 5 },
        { 7, 4, 3 },
        { 6, 2, 1 },
    };
    show( data );
    printf( "Score is %d", calc_score( data ) );
#endif
#if 1
    // Brute-force scan of the all possible combinations.
    // Some of them (containing zeroes) will be ignored inside of calc_score() function.
    int max_score = 0;
    for( int i = 0; i < 1e9; i++ )
    {
        int score = calc_score( i );
        if( score > max_score )
        {
            max_score = score;
        }
    }
    printf( "The best possible score is %d\n", max_score );
#endif
    return( 0 );
}

 

ps. I don't normally use plain ANSI C, rather C++, but it grew and grew while writing..

 

Edited February 6, 20196 yr by Sensei

Yes,

These are the two combinations !

9	8	4		984	976	288	378	165
7	5	3		753	852	105	80	216
6	2	1		621	431	12	12	336
				2358	2259	405	470	717	3025
9	7	6		976	984	378	288	165
8	5	2		852	753	80	105	216
4	3	1		431	621	12	12	336
				2259	2358	470	405	717	3025

You are very good in programming !

I have so far been able to use Excel for these Puzzles with success !