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Getting 8 (Posted on 2019-08-11) Difficulty: 4 of 5
ABCDE/FGHJ=8

i. How many solutions are there ?
ii. How many solutions are there, zeros excluded?
iii. Provide the values with the highest A.
iv. Provide the values with the lowest A.

See The Solution Submitted by Ady TZIDON    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
comp soln | Comment 2 of 42 |
with 0
76 min 1 max 7

w/o 0 
46 min 2 max 7
rabbit-3:~ lord$ xc
cnt =    1 max = 1 min = 1 8 = 16584/2073
cnt =    2 max = 1 min = 1 8 = 18456/2307
cnt =    3 max = 1 min = 1 8 = 18760/2345
cnt =    4 max = 2 min = 1 8 = 24568/3071
cnt =    5 max = 2 min = 1 8 = 24856/3107
cnt =    6 max = 2 min = 1 8 = 25408/3176
cnt =    7 max = 2 min = 1 8 = 25496/3187
cnt =    8 max = 2 min = 1 8 = 27608/3451
cnt =    9 max = 3 min = 1 8 = 32568/4071
cnt =   10 max = 3 min = 1 8 = 32856/4107
cnt =   11 max = 3 min = 1 8 = 36712/4589
cnt =   12 max = 3 min = 1 8 = 36728/4591
cnt =   13 max = 3 min = 1 8 = 37208/4651
cnt =   14 max = 3 min = 1 8 = 37512/4689
cnt =   15 max = 3 min = 1 8 = 37528/4691
cnt =   16 max = 3 min = 1 8 = 38016/4752
cnt =   17 max = 3 min = 1 8 = 38120/4765
cnt =   18 max = 3 min = 1 8 = 38152/4769
cnt =   19 max = 4 min = 1 8 = 41896/5237
cnt =   20 max = 4 min = 1 8 = 42968/5371
cnt =   21 max = 4 min = 1 8 = 46312/5789
cnt =   22 max = 4 min = 1 8 = 46328/5791
cnt =   23 max = 4 min = 1 8 = 46712/5839
cnt =   24 max = 4 min = 1 8 = 47136/5892
cnt =   25 max = 4 min = 1 8 = 47328/5916
cnt =   26 max = 4 min = 1 8 = 47368/5921
cnt =   27 max = 5 min = 1 8 = 50184/6273
cnt =   28 max = 5 min = 1 8 = 50728/6341
cnt =   29 max = 5 min = 1 8 = 51024/6378
cnt =   30 max = 5 min = 1 8 = 51072/6384
cnt =   31 max = 5 min = 1 8 = 51832/6479
cnt =   32 max = 5 min = 1 8 = 53928/6741
cnt =   33 max = 5 min = 1 8 = 54312/6789
cnt =   34 max = 5 min = 1 8 = 54328/6791
cnt =   35 max = 5 min = 1 8 = 54712/6839
cnt =   36 max = 5 min = 1 8 = 56184/7023
cnt =   37 max = 5 min = 1 8 = 56248/7031
cnt =   38 max = 5 min = 1 8 = 56328/7041
cnt =   39 max = 5 min = 1 8 = 56824/7103
cnt =   40 max = 5 min = 1 8 = 56832/7104
cnt =   41 max = 5 min = 1 8 = 56984/7123
cnt =   42 max = 5 min = 1 8 = 58104/7263
cnt =   43 max = 5 min = 1 8 = 58416/7302
cnt =   44 max = 5 min = 1 8 = 58496/7312
cnt =   45 max = 5 min = 1 8 = 58912/7364
cnt =   46 max = 5 min = 1 8 = 59328/7416
cnt =   47 max = 5 min = 1 8 = 59368/7421
cnt =   48 max = 6 min = 1 8 = 60184/7523
cnt =   49 max = 6 min = 1 8 = 60248/7531
cnt =   50 max = 6 min = 1 8 = 60328/7541
cnt =   51 max = 6 min = 1 8 = 62504/7813
cnt =   52 max = 6 min = 1 8 = 63152/7894
cnt =   53 max = 6 min = 1 8 = 63528/7941
cnt =   54 max = 6 min = 1 8 = 65072/8134
cnt =   55 max = 6 min = 1 8 = 65392/8174
cnt =   56 max = 6 min = 1 8 = 65432/8179
cnt =   57 max = 6 min = 1 8 = 65704/8213
cnt =   58 max = 6 min = 1 8 = 67152/8394
cnt =   59 max = 6 min = 1 8 = 67320/8415
cnt =   60 max = 6 min = 1 8 = 67352/8419
cnt =   61 max = 6 min = 1 8 = 67512/8439
cnt =   62 max = 7 min = 1 8 = 71456/8932
cnt =   63 max = 7 min = 1 8 = 71536/8942
cnt =   64 max = 7 min = 1 8 = 71624/8953
cnt =   65 max = 7 min = 1 8 = 71632/8954
cnt =   66 max = 7 min = 1 8 = 73248/9156
cnt =   67 max = 7 min = 1 8 = 73264/9158
cnt =   68 max = 7 min = 1 8 = 73456/9182
cnt =   69 max = 7 min = 1 8 = 74528/9316
cnt =   70 max = 7 min = 1 8 = 74568/9321
cnt =   71 max = 7 min = 1 8 = 74816/9352
cnt =   72 max = 7 min = 1 8 = 75328/9416
cnt =   73 max = 7 min = 1 8 = 75368/9421
cnt =   74 max = 7 min = 1 8 = 76184/9523
cnt =   75 max = 7 min = 1 8 = 76248/9531
cnt =   76 max = 7 min = 1 8 = 76328/9541
rabbit-3:~ lord$ xc
cnt =    1 max = 2 min = 2 8 = 25496/3187
cnt =    2 max = 3 min = 2 8 = 36712/4589
cnt =    3 max = 3 min = 2 8 = 36728/4591
cnt =    4 max = 3 min = 2 8 = 37512/4689
cnt =    5 max = 3 min = 2 8 = 37528/4691
cnt =    6 max = 3 min = 2 8 = 38152/4769
cnt =  7 max = 4 min = 2 8 = 41896/5237
cnt =    8 max = 4 min = 2 8 = 42968/5371
cnt =    9 max = 4 min = 2 8 = 46312/5789
cnt =   10 max = 4 min = 2 8 = 46328/5791
cnt =   11 max = 4 min = 2 8 = 46712/5839

cnt =   12 max = 4 min = 2 8 = 47136/5892

cnt =   13 max = 4 min = 2 8 = 47328/5916
cnt =   14 max = 4 min = 2 8 = 47368/5921
cnt =   15 max = 5 min = 2 8 = 51832/6479
cnt =   16 max = 5 min = 2 8 = 53928/6741
cnt =   17 max = 5 min = 2 8 = 54312/6789
cnt =   18 max = 5 min = 2 8 = 54328/6791
cnt =   19 max = 5 min = 2 8 = 54712/6839
cnt =   20 max = 5 min = 2 8 = 56984/7123
cnt =   21 max = 5 min = 2 8 = 58496/7312
cnt =   22 max = 5 min = 2 8 = 58912/7364
cnt =   23 max = 5 min = 2 8 = 59328/7416
cnt =   24 max = 5 min = 2 8 = 59368/7421
cnt =   25 max = 6 min = 2 8 = 63152/7894
cnt =   26 max = 6 min = 2 8 = 63528/7941
cnt =   27 max = 6 min = 2 8 = 65392/8174
cnt =   28 max = 6 min = 2 8 = 65432/8179
cnt =   29 max = 6 min = 2 8 = 67152/8394
cnt =   30 max = 6 min = 2 8 = 67352/8419
cnt =   31 max = 6 min = 2 8 = 67512/8439
cnt =   32 max = 7 min = 2 8 = 71456/8932
cnt =   33 max = 7 min = 2 8 = 71536/8942
cnt =   34 max = 7 min = 2 8 = 71624/8953
cnt =   35 max = 7 min = 2 8 = 71632/8954
cnt =   36 max = 7 min = 2 8 = 73248/9156
cnt =   37 max = 7 min = 2 8 = 73264/9158
cnt =   38 max = 7 min = 2 8 = 73456/9182
cnt =   39 max = 7 min = 2 8 = 74528/9316
cnt =   40 max = 7 min = 2 8 = 74568/9321
cnt =   41 max = 7 min = 2 8 = 74816/9352
cnt =   42 max = 7 min = 2 8 = 75328/9416
cnt =   43 max = 7 min = 2 8 = 75368/9421
cnt =   44 max = 7 min = 2 8 = 76184/9523
cnt =   45 max = 7 min = 2 8 = 76248/9531
cnt =   46 max = 7 min = 2 8 = 76328/9541
rabbit-3:~ lord$ more xc.f
        program xc
        implicit none
        integer a,b,c,d,e,f,g,h,j,z,cnt,num,den,min,max
        max=0
        min=9
        cnt=0
        z=1
        do    a=z,9                      
                   
        do 8  b=z,9        
        if(b.eq.a)go to 8
                   
        do 7  c=z,9        
        if(c.eq.a.or.c.eq.b)go to 7         
                   
        do 6  d=z,9        
        if(d.eq.a.or.d.eq.b.or.d.eq.c)go to 6
                   
        do 5  e=z,9
        if(e.eq.a.or.e.eq.b.or.e.eq.c.or.e.eq.d)go to 5 
        num=a*10000+b*1000+c*100+d*10+e

        do 4  f=z,9
        if(f.eq.a.or.f.eq.b.or.f.eq.c.or.f.eq.d.or. 
        1  f.eq.e)go to 4

        do 3  g=z,9
        if(g.eq.a.or.g.eq.b.or.g.eq.c.or.g.eq.d.or.
        1  g.eq.e.or.g.eq.f)go to 3

        do 2  h=z,9
        if(h.eq.a.or.h.eq.b.or.h.eq.c.or.h.eq.d.or.
        1  h.eq.e.or.h.eq.f.or.h.eq.g)go to 2

        do 1  j=z,9
        if(j.eq.a.or.j.eq.b.or.j.eq.c.or.j.eq.d.or.
        1  j.eq.e.or.j.eq.f.or.j.eq.g.or.j.eq.h)go to 1
        den=f*1000+g*100+h*10+j
      if(8*den.eq.num)then
                cnt=cnt+1
                if(a.gt.max)max=a
                if(a.lt.min)min=a
                print 100,cnt,max,min,num,den
100             format('cnt =' ,i5,1x,'max = ',i1,1x,
        1       'min = ',i1,1x,'8 = ',i5,'/',i4)
                endif
1       enddo
2       enddo
3       enddo
4       enddo  
5       enddo
6       enddo
7       enddo  
8       enddo
      enddo
      end        

xc.f (END)

Edited on August 11, 2019, 2:00 pm
  Posted by Steven Lord on 2019-08-11 12:30:03

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