How to Cheat with Math – The Russian Cards Problem
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How to Cheat with Math – The Russian Cards Problem
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Re: How to Cheat with Math – The Russian Cards Problem
#2[deleted]
Re: How to Cheat with Math – The Russian Cards Problem
#3Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
Re: How to Cheat with Math – The Russian Cards Problem
#4The advised reader could devise a solution using public / private key where:
- Alice communicates her public key
- Bob communicates his
- Alice encoders her cards with Bob’s public key
- Bob does the same
Problem solved!
Re: How to Cheat with Math – The Russian Cards Problem
#5Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
Is the modulo required? Is just "The sum of my cards is x" sufficient?
Re: How to Cheat with Math – The Russian Cards Problem
#6Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
Is the modulo required? Is just "The sum of my cards is x" sufficient?
Yes. For instance, if a player says the sum of their cards is 3, Eve immediately knows they have cards 0, 1 and 2.
Re: How to Cheat with Math – The Russian Cards Problem
#7Re: How to Cheat with Math – The Russian Cards Problem
#8Does "the sum of my cards modulo 7 is [x]" work? It should let Bob know what the missing card is but I can't tell if it conveys sufficiently little information to Eve for it to count.
The article's definition of not revealing information is a bit unclear, but if we understand it as Eve not knowing who holds any single card, your solution seems to work. At least assuming the following code is correct :)
import itertools import functools
for eve_card in range(7): cards_left = set(range(7)) cards_left.remove(eve_card)
mod_to_cards = [[], [], [], [], [], [], []]
for c in itertools.combinations(cards_left, 3):
mod = sum(c) % 7
mod_to_cards[mod].append(set(c))
for combs in mod_to_cards:
i = functools.reduce(lambda x, y: x.intersection(y), combs)
if len(i) != 0:
print("intersection", eve_card, combs, i)
u = functools.reduce(lambda x, y: x.union(y), combs)
if len(u) != 6:
print("union", eve_card, combs, u)