In fact, I finished this assignment about 2 hours although this examination must require within one and a half hours.

import sys

vs = {}
for i in range(1,len(sys.argv)):
    a = sys.argv[i].split("=")
    vs[a[0]] = a[1]
hist = {}
num=5 # num of cards
ol=[]
for i in range(1,num+1):
    ol.append(i)
a = int(vs["A"])
b = int(vs["B"])
c = int(vs["C"])

def simpleGuess(l,o1,o2):
    if o1 in l:
        l.remove(o1)
    if o2 in l:
        l.remove(o2)
    if len(l)==0:
        return '?' 
    if (max(l) < o1 and max(l) < o2):
        return 'MIN'
    elif (min(l) > o1 and min(l) > o2):
        return 'MAX'
    else:
        b = True
        for e in l:
            if (e > o1 and e < o2) or (e > o2 and e < o1) \
                or (e > o1 and e < o2) or (e > o2 and e < o1):
                continue
            else:
                b = False
                break
        if (b == True):
            return 'MID'
        return '?' 

def guess(nl,nl2):
    for e in nl: 
        tl = list(nl)
        tl.remove(e)
        b = True
        for i in range(len(tl)-1):
            if (abs(tl[i]-tl[i+1])==1):
                continue
            else:
                b = False
                break
        if (b and (e in nl2)):
            nl2.remove(e)

# a
out = ""
ret = simpleGuess(list(ol),b,c)
out = 'A =>'+ret
if (ret!='?'):
    print(out)
    exit()
else:
    out = out + ", "

while(1):
    # b 
    nl2 = list(ol)
    nl = list(ol)
    nl.remove(c)
    guess(nl,nl2)
    ret = simpleGuess(nl2,a,c)
    out = out + 'B =>'+ret
    if (ret!='?'):
        print(out)
        exit()
    else:
        out = out + ", "
    # c 
    nl = list(ol)
    nl2 = list(ol)
    nl.remove(a)
    guess(nl,nl2)
    ret = simpleGuess(nl2,a,b)
    out = out + 'C =>'+ret
    if (ret!='?'):
        print(out)
        exit()
    else:
        out = out + ", "
    # a 
    nl = list(ol)
    nl2 = list(ol)
    nl.remove(b)
    guess(nl,nl2)
    ret = simpleGuess(nl2,b,c)
    out = out + 'A =>'+ret
    if (ret!='?'):
        print(out)
        exit()
    else:
        out = out + ", "

$ python a.py A=1 B=4 C=5 
A =>MIN
$ python a.py A=1 B=2 C=4
A =>?, B =>MID
$ python a.py A=4 B=3 C=2
A =>?, B =>?, C =>MIN
$ python a.py A=1 B=3 C=2
A =>?, B =>MAX
$ python a.py A=1 B=3 C=5
A =>?, B =>MID

BTW, RCO engineers seem to hate PHPers...

The answer to past coding examination of RCO with python

Refs.