simpsons-bruteforce.c

/* reimplementation of simpsons-bruteforce.lua in c for practice */

#include <stdio.h>

#define INCREMENT 5

#define a_part 210
#define a_whole 300
#define b_part 180
#define b_whole 300

int main(void) {
    unsigned int a_full_part, a_full_whole, b_full_part, b_full_whole;
    unsigned int a_part_part, a_part_whole, b_part_part, b_part_whole;
    float a_full_proportion, a_part_proportion, b_full_proportion, b_part_proportion;
    
    for (a_full_part = 0; a_full_part <= a_part; a_full_part = a_full_part + INCREMENT) {
        a_part_part = a_part - a_full_part;
        
        for (a_full_whole = 0; a_full_whole <= a_whole; a_full_whole = a_full_whole + INCREMENT) {
        a_part_whole = a_whole - a_full_whole;
        
            for (b_full_part = 0; b_full_part <= b_part; b_full_part = b_full_part + INCREMENT) {
                b_part_part = b_part - b_full_part;
                
                for (b_full_whole = 0; b_full_whole <= b_whole; b_full_whole = b_full_whole + INCREMENT) {
                    b_part_whole = b_whole - b_full_whole;
                    
                    if ((a_part_whole > 0) && (a_full_whole > 0) && (b_part_whole > 0) && (b_full_whole > 0)) {
                        
                        a_full_proportion = (float)a_full_part / a_full_whole;
                        a_part_proportion = (float)a_part_part / a_part_whole;
                        b_full_proportion = (float)b_full_part / b_full_whole;
                        b_part_proportion = (float)b_part_part / b_part_whole;
                        
                        if ((a_full_proportion < 1) && (a_part_proportion < 1) && (b_full_proportion < 1) && (b_part_proportion < 1)
                            && (b_full_proportion > a_full_proportion) && (b_part_proportion > a_part_proportion)) {
                            printf("a full: %4d/%4d, b full: %4d/%4d\n",a_full_part,a_full_whole,b_full_part,b_full_whole);
                            printf("a part: %4d/%4d, b part: %4d/%4d\n",a_part_part,a_part_whole,b_part_part,b_part_whole);
                            printf("\n");
                        }
                        
                    }
                    
                }
            }
        }
    }
}

simpsons-bruteforce.lua

#!/usr/bin/lua

--[[
    
    quick and messy script to bruteforce chapter 3 exercise #40, the simpsons
    paradox problem, of the stats: modeling the world textbook

    how this script works:
    1. iterate through all possible proportions for company a full time, company
       a part time, company b full time, and company b part time by iterating
       through all possible combinations of their numerators and denominators
    2. if:
           b full time proportion > a full time proportion 
       and:
           b part time proportion > a part time proportion
       then print the individual numerators and denominators. these are the
       answers to the question.
    
--]]

a_part=210
a_whole=300

b_part=180
b_whole=300

increment=5

function printf(s,...)
    return io.write(string.format(s,...))
end

function isinteger(num)
    if math.floor(num)/num == 1 then
        return true
    else
        return false
    end
end

-- no zeroes
function checknumbers(...)
    for _,num in pairs({...}) do
        if --[[not isinteger(num) or]] num == 0 then
            return false
        end
    end
    return true
end

-- no >1 proportions
function checkproportions(...)
    for _,proportion in pairs({...}) do
        if proportion > 1 then
            return false
        end
    end
    return true
end

for a_full_part=0,a_part,increment do
    a_part_part=a_part-a_full_part
    
    for a_full_whole=0,a_whole,increment do
        a_part_whole=a_whole-a_full_whole
        
        for b_full_part=0,b_part,increment do
            b_part_part=b_part-b_full_part
            
            for b_full_whole=0,b_whole,increment do
                b_part_whole=b_whole-b_full_whole
                
                a_full_proportion=a_full_part/a_full_whole
                a_part_proportion=a_part_part/a_part_whole
                b_full_proportion=b_full_part/b_full_whole
                b_part_proportion=b_part_part/b_part_whole
                
                --print(check(a_full_part,a_full_whole,b_full_part,b_full_whole,a_part_part,a_part_whole,b_part_part,b_part_whole),a_full_part,a_full_whole,b_full_part,b_full_whole,a_part_part,a_part_whole,b_part_part,b_part_whole)
                if (b_full_proportion > a_full_proportion) and (b_part_proportion > a_part_proportion)
                    and checknumbers(a_full_part,a_full_whole,b_full_part,b_full_whole,a_part_part,a_part_whole,b_part_part,b_part_whole) 
                    and checkproportions(a_full_proportion,a_part_proportion,b_full_proportion,b_part_proportion) then
                    printf("a full: %4d/%4d, b full: %4d/%4d\n",a_full_part,a_full_whole,b_full_part,b_full_whole)
                    printf("a part: %4d/%4d, b part: %4d/%4d\n",a_part_part,a_part_whole,b_part_part,b_part_whole)
                    printf("\n")
                end
                
            end
        end
    end
end