# Solution to the Zen Archery problem by leonardo maffi, V1.1, Feb 24 2007

# Problem URL: www.merriampark.com/comb.htm
# Given the following 24 numbers taken 5 at a time, which unique combinations
# adds up to 200?
d = [97,101,139,41,37,31,29,89,23,19,8,13,131,19,
     73,97,19,139,79,67,61,17,113,127]

import csp # http://www.fantascienza.net/leonardo/so/csp.zip

"""
# Wrong version:
p = csp.Problem("RecursiveBacktracking")
p.addvars("abcde", d)
p.alldifferent()
p.addrule("a+b+c+d+e == 200")
sols = p.solutions()
print map(list, set(frozenset(s[v] for v in "abcde") for s in sols))
"""

p = csp.Problem()
p.addvars("abcde", enumerate(d))
p.alldifferent()
# This is the faster rule I have found
p.addrule(lambda a,b,c,d,e: a[1]+b[1]+c[1]+d[1]+e[1]==200)
sols, t = csp.timing(p.solutions)
sols2 = (tuple(sorted(s[v][1] for v in "abcde")) for s in sols)
sols3 = sorted(set(sols2))
print t, "secs", len(sols3), "solutions:", sols3