# Another math problem...

qwweeeit qwweeeit at yahoo.it
Sat Mar 5 01:56:53 CET 2005

```Another math problem easier to solve by hand, but, IMHO, difficult to
program in a concise way like the solution of Bill Mill
(linalg_brute.py) to the problem of engsol.

I appreciated very much the Bill Mill's solution and that inspired in
a certain way the solution for my problem.

# Problem and solution:

#  ab *  cb = dab             35 *  26 = 936
#   +     +     -              +     +     -
# ifd + chg = eaf            179 + 258 = 437
# ---------------            ---------------
# cih + cge = edd            215 + 284 = 499

>From that you can get 6 equations:

# equation n. 1 :      (10a+b) *     ( 10c+b) = 100d+10a+b
# equation n. 2 :  100i+  f d  +  100c+  h g  =    e+  a f
# equation n. 3 :     c+  i h  +     c   g e  =    e   d d
# equation n. 4 :      (  a b) +     i   f d  =    c   i h
# equation n. 5 :      (  c b) +     c   h g  =    c   g e
# equation n. 6 :     d+  a b  -     e   a f  =    e   d d

(I removed most of digit part  to enhance the variables).

My solution:

def Hund(w):                      # hundreths
.   return int(w/100)
def Ten2(w):                      # tenths for 2 digits
.   return int(w/10)
def Ten(w):                       # tenths for 3 digits
.   return int((w%100)/10)
def Unit(w):                      # units
.   return w%10

nc = range(100,1000)      # range of 3 digits numbers
nd = range(10,100)        # range of 2 digits numbers

def eq_1():
.    return [(x,y,z) for x in nd \
.                    for y in nd \
.                    for z in nc \
.                    if  x*y-z   == 0 \
.                    and Unit(x) == Unit(y) \
.                    and Unit(x) == Unit(z) \
.                    and Ten2(x) == Ten(z) \
.                    and Ten2(x) != Ten2(y) ]

lResult1=eq_1()
print lResult1

>From the results you can choose other equations to treat with the same
approach.

I know it's a rather long process.. but that is the best I can do.

```