gistfile1.txt

# Solution to Lucy's secret number puzzle, from
# http://datagenetics.com/blog/june12018/index.html

import collections

# how are the four questions answered for this number?
def signature(n):
    return ( n % 2 == 0
           , n % 3 == 0
           , n % 5 == 0
           , n % 7 == 0
           )

# For each "signature", what numbers share that signature?
signatures = collections.defaultdict(list)
for i in range(1, 100):
    signatures[signature(i)] += [i]

# What signatures have just one number each?
[(k, v) for k, v in signatures.items() if len(v) == 1]

# -> [((False, False, True, True), [35]), ((True, False, True, True), [70])]

# The solution is obvious by inspection: if you heard the first question and answer,
# you know the number. If the answer was "Yes" (i.e. True), the number is 70.