
NSA's Puzzle Periodical - edgartaor
https://www.nsa.gov/news-features/puzzles-activities/
======
IIAOPSW
Ava always guesses the same color as Bobs forehead. Bob always guesses the
opposite color as Ava's forehead.

~~~
im4w1l
For the four people puzzle. Assign every suit a number 0-3. All four people
guess differently what the sum of all the cards is modulo 4, meaning exactly
one person will get it right. Using the sum and the view of the other cards
the one who guessed right can work out their own card.

~~~
philbarr
It seems that we could expand this for n people with n choices.

So in the first case where there are only 2 people and 2 colours, they assign,
say 0 to black and 1 to red. Then they each sum up the other choices they can
see (which happens to be only one other choice in this case) plus their own
assigned number (0 or 1) and answer that modulo 2.

Er..I think...?

~~~
brian_cloutier
Yeah, that sounds right. Through that lens, the first problem is a special
case of the second problem.

------
bitwize
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Find out by logging in to our totally legit, completely innocuous, not in any
way a honeypot that collects extensive info on you, puzzle site!

~~~
Animats
GCHQ has been known to do this for recruiting purposes.[1]

[1]
[https://web.archive.org/web/20130912120456/https://canyoufin...](https://web.archive.org/web/20130912120456/https://canyoufindit.co.uk/)

~~~
Moter8
The german BND too:

[https://www.bnd.bund.de/DE/Karriere/Reversing_Challenge/Reve...](https://www.bnd.bund.de/DE/Karriere/Reversing_Challenge/Reversing_Challenge_node.html)

German video resolving the first of three challenges:
[https://www.youtube.com/watch?v=mZH094d0M6A](https://www.youtube.com/watch?v=mZH094d0M6A)

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pokstad
August 2016:
[https://en.m.wikipedia.org/wiki/Hat_puzzle](https://en.m.wikipedia.org/wiki/Hat_puzzle)

~~~
dangero
"The players may not communicate in any way" \- It seems to me that all the
answers are a form of communication. In fact the dictionary defines
communicate as, "share or exchange information."

~~~
martinko
What a joke: "find a strategy for the players to determine the colours of
their hats based on the hats they see and what the other players do"

I interpreted it in the same way as you did - communication on any level is
not allowed. If there is no sharing of information then I think it is
impossible to solve the puzzle.

~~~
facepalm
It is possible without communication (also without seeing what the other
players do).

~~~
dangero
How so?

~~~
facepalm
Some answers have been posted already.

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x0137294744532
The solution to the 4 person problem is actually pretty simple. Let's assume
that we know the answer to the 2 person problem. We have 4 persons; A, B, C
and D. At first the persons guess their colour (without revealing it of
course) based on their direct neighbor. So for instance:

    
    
        A <-----> B
        
        
        C <-----> D
    

A and B being neighbors, they guess their colours based on the solution of the
2 persons problem. Same goes for C and D. Without loss of generality, let's
assume C guesses correctly his card colour. Since he can see the cards of A
and B, he knows who will guess their colour correctly. For instance, if they
have the same colour, A will guess correctly, if not, then B will guess
correctly. Without loss of generality, let's assume A guesses correctly his
card colour. He then sees that C will guess correctly.

The participants agreed beforehand that clubs and hearts are associated with 0
while diamonds and spades are associated with 1. A and C now apply the
solution to the 2 person problem to guess their shape group (either (diamonds
or spades) or (clubs or hearts)):

    
    
        A       B
        |
        |
        C       D
    

It is guaranteed that at least one has guessed the shape group correctly.
Since they both guessed correctly the color, it is guaranteed that one of them
will guess the shape correctly.

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glu
I'm more of a Car Talk "Puzzler" type of guy.

~~~
blueintegral
"If you think you know the answer, write it on the back of your classified one
time pad key and send it to: NSA, Box 35 Fort Meade (our fair city) Maryland".

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cwilkes
Use this one weird trick to win the guess what card is on my forehead game.
Casinos hate it!

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tn13
Are there any puzzles that help you master "plausible deniability" much better
?

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Kapow
Some of these are poorly worded. Why does the answer to the May one keep
talking about 30 seconds passing when the only time mentioned in the problem
is 30 minutes? 30 seconds gives Nick at least 10 seconds per possible
solution, he should have tried them all by then.

It should talk about the number of tries so far (one each), the length of time
it took is irrelevant. But why are they even taking turns when they have
separate padlocks and could easily brute-force it? I get the concept they're
going for but the premise doesn't fit and just confuses things.

~~~
XeO3
Yeah. I didn't get what the big deal was about it until I read the 30 second
and turns he mentioned in his explanation.

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advisedwang
The NSA also has (had?) an internal puzzle in there cryptolog internal
magazine. Some have been declassfied at [https://www.nsa.gov/news-
features/declassified-documents/cry...](https://www.nsa.gov/news-
features/declassified-documents/cryptologs/). An example of their puzzles:
[https://david.newgas.net/nsa-puzzle/](https://david.newgas.net/nsa-puzzle/)

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cdevs
It said no communication during but you could devise a strategy before play.
What I would do on the first challenge is say I would write down the opposite
color of what I see and tell the other person the write down the same color
they see so you will definitely at least win $50 "or 100$ if you have the same
color". For the suite challenge do the same strategy but split 2 people write
down the same suite and have a plan for the other 2 to pick what they don't
see.

~~~
cbgb
Coincidentally enough, this was a submitted puzzler to the NPR syndicated show
"Car Talk," except there were 10 men in a line wearing black or white hats.
The goal was to determine the optimal strategy for guessing hat colors.

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flashman
Orienting the cards vertically or horizontally would count as communication,
wouldn't it? Otherwise this would be trivial.

~~~
cwilkes
I'm not sure how orienting the card that is on your own head would help. You
don't know what it is.

That being said the method of "Bob always tells the truth, Alice lies" is sort
of a card orientation way for two people. Alice puts her card up sideways and
Bob knows that to mean he should tell the truth. Likewise Bob doesn't rotate
his and Alice knows to lie.

However that only works with two people and they have opposite spins.

Maybe it can work with more than two and you have two rounds of guessing. Also
you need to know that you have differing spins.

~~~
flashman
You orient the card based on the other player's card, for their benefit.
That's why I think it would be against the rules - it's the same as if you
held up fingers or made a face, it's communication.

Bruce and Ava decide to put the card horizontally if they see a red card, or
vertically if it's black. If Bruce sees a vertical card, he knows Ava sees a
red card on his head.

In the game of four, the players decide one of them will guess, and two others
will communicate information in binary:

horizontal, horizontal: hearts

horizontal, vertical: diamonds

vertical, horizontal: spades

vertical, vertical: clubs

However this latter method only requires three players, not four. But it is
similar to how professional bridge players cheat, by communicating their hand
(which is hidden from their partner) with secret signals:
[http://www.newyorker.com/magazine/2016/03/07/the-cheating-
pr...](http://www.newyorker.com/magazine/2016/03/07/the-cheating-problem-in-
professional-bridge)

~~~
cwilkes
Wow, thanks for that link about cheating in bridge. Spent hours going over
that and stories on [http://bridgewinners.com/](http://bridgewinners.com/)

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fractalb
The answer is pretty simple.

1\. The strategy is that they should agree to write down the same
colour(either red or black), irrespective of what they see on the opposite
persons forehead

2\. Same as above. This time all of them should agree to write any single
suit.

By probability, at least one of them will get it right.

[Edit]: Didn't put it correctly before

~~~
faaabio1618
1 They should write their own color, so this is not a winning strategy.
[Spoiler] As stated by other the winning strategy is that one says always the
other person's color and the other say the opposite. That's because or the
color are the same or are different.

~~~
fractalb
You're right

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malingo
Reminds me of "ponder this" from IBM research:
[https://researchweb.watson.ibm.com/haifa/ponderthis/index.sh...](https://researchweb.watson.ibm.com/haifa/ponderthis/index.shtml)

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curiousgal
The April one was.. disappointing.

~~~
ktta
The June one too. A simple three if then statements can solve the problem
easily even increasing the 1000 coins to a number physically possible by the
ship to hold.

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ForFreedom
Come back tomorrow as in Sep 1, 2017 for the answer I suppose.

There I cracked that one :)

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pcool_deathel
Make Bruce guess opposite of what he sees on Ava and Ava guess same color as
what she sees on Bruce. This covers atleast one correct guess for all for
Cases BB, RR, BR, RB.

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zazaalaza
[https://github.com/zazaalaza/napp](https://github.com/zazaalaza/napp)

see my solution here

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Cogito
For the July one:

Always go first.

Assuming the table is symmetrical around only one point, the centre of the
table, place the first coin on that point.

Every move after that place your coin in the location directly opposite the
last coin played, the mirrored location around the point of symmetry.

Since you are always playing a symmetrical position, you know that there will
always be a space available for you after the previous coin was played.

[edit] looks like the answer on the site is almost the exact wording as mine
:)

~~~
datr
This is actually very similar to a question I was asked when interviewing to
read Maths at Oxford. In the Oxford version, your brother and you are also
playing a game. You have a 2-dimensional block of chocolate with a poison
piece somewhere in the block. The poison piece is bright green to the eye. You
each take it in turn to break off some chocolate (you have to follow the rows
and columns of the chocolate, and the break must be a single break). To win
you must avoid eating the poison piece and end the game by handing it to your
brother. You have the choice of going first or second? When should you choose
either?

~~~
im4w1l
Nim in disguise

------
teekert
_Come back tomorrow to see the answer!_

But where?

