Unnecessary breakage

Yesterday I was watching a bunch of my friends play a word association party game.  The basic idea is that you have two teams, and on each team one person is the caller.  There are twenty five cards with random words on them laid out on the table, and the caller has to try to give clues to get their teammates to guess their own cards without guessing the opponent's.  Teams alternate giving clues until one team discovers all of their own cards.  Each clue has to be a word and a number, and the obvious thing the numbers are supposed to mean is 'how many cards match this clue'.

So if the cards were

Dog
Cat
Hamburger

I might say "Animal, 2" to get my partner to guess Dog and Cat.

I started immediately thinking about how to optimize the clue giving to improve my odds.  The people playing were all just playing like the rulebook suggests, getting 1-2 cards each turn.  Fairly quickly I realized the optimal solution to this problem is to simply use an 18 digit number after the word to describe exactly which cards were the ones to pick.  Each set of 2 digits describes a particular card in the group, so the word itself doesn't even matter, the 18 digit number tells your partner all 9 cards they need to pick to win the game.

The rulebook does not suggest that this strategy would be against the rules.  They apparently hadn't counted on me trying to ruin a perfectly fine party game by applying thinking to the problem.

However, my solution doesn't simply provide a really good strategy - it outright ruins the game.  Given this, I decided to try to think of some more cool strategies that were powerful but which didn't render the game a coinflip nor completely remove the whole word association aspect.  One thing I decided is that the number you give definitely has to be a single digit integer.  Allowing people to go up to 9 to establish signals should definitely give me some cool design space, but hopefully will allow the players to still play the game.

What I was thinking with this is just leading with the assumption that any number you give above 0 is a signal as to card placement.  So if I said "Animal, 5" my team should assume that they should find precisely 2 cards associated with Animal and then pick the fifth unknown card in order.  This loses out if you can actually clue 4 cards at once with a single category, but lets you get 3 cards on the great majority of your clues, and I suspect that is good enough.  You could use 0 as a signal to just pick the single card associated with the word you state, which seems like a thing you want to have in your arsenal but which is pretty bad.

By my way of thinking, the power to nearly always get 3 is the ticket to winning.  If you screw it up, fine, but aggressively going after good turns is going to be the way to win the majority of the games.

In my head this kind of thinking means that people who make party games should totally hire me to review their rule sections to write things to prevent shenanigans like this.  I suspect what it really means is that I don't get how people play party games at all.

Know your role

As one professional wrestler so regularly informed his enemies, it is important to know your role.  This is particularly true when you are part of a team and there are a variety of tasks to perform that require different sorts of talents.  While people often want to work with others just like themselves there is a huge benefit in having a broad spectrum of abilities, skills, and even approaches to problems when facing an unknown challenge.

This past weekend I was involved in a pair of escape room challenges.  This is a puzzle composed of a number of rooms with many stages that is tackled by a small group of people - in my case 6 and 8 individuals for the two respective games.  The first was themed around the idea of a diamond heist where my group had to break through a series of locked doors using keys, codes, and odd puzzles of all sorts.  The second was set in a mocked up Japanese house that had been the site of a variety of horrible deaths and was filled with plenty of scenes that would fit in nicely in a horror film.  In that one we had free run of the house and had to solve a large number of puzzles in any order to advance to the final challenge.

It was *amazing*.  Not the cheapest entertainment around as it was $40 for two hours but so worth it for the experience.  There were some folks in my group who genuinely found the horror elements of the second game difficult to deal with because the company that did it (Escape Games near Downsview station in Toronto) did a great job on the aesthetics and ambience.  Unsurprisingly I was so engrossed in trying to win the game within the 1 hour allotted I barely registered any emotional reaction to the scenes except to note that they were well done.

In nearly all random groups of people trying such a task I would be the puzzle nerd.  I would expect to be tasked with sitting down grinding out codes or working out interfaces.  However the group I went with had a huge number of hardcore game geeks with strong technical backgrounds so there was no need for me to play that role as it was thoroughly saturated.  I looked around at those playing with me and realized that in this particular group I people I was the physical one, the person who should be running around, yanking on things, bashing myself into objects, and generally trying to solve all of the meatspace portions of the games.  I took to this role so thoroughly that whenever I encountered a new piece of an intellectual puzzle I almost universally handed it to the nearest person and ran off to go push on some other piece of the environment.  As Sthenno put it when I described it "In that group you were the jock!"

It worked beautifully.  I was the one who leapt into the tunnel on my belly, scooting forward under the laser.  I yanked furniture, found secret tunnels, spun wheels, slid things, discovered hidden materials, and jumped into dark, mysterious holes to see what was there.  It was glorious.  So while I feel I played the game pretty well the thing I am most pleased about was how I played the metagame.  There were definitely times when I was just wasting my effort poking at random stuff that had nothing to do with anything while my team solved puzzles but all the things I did do pushed us forward.  When you are taking a specific role in a game like this it is important to accept that sometimes you will be the hero and sometimes you will stand around being useless and you must keep focused on doing what you are good at rather than hunting for all the glory.

I highly recommend this genre of games in general, and Escape Games in particular.  If you do give it a try I definitely suggest going with a group with varied skills and talking about each person's specialties so that everyone can know their role.

A puzzle

Randall Munroe (the writer of xkcd) posed an interesting problem on G+ a short while ago I thought I would share.  Quote:

You have a rectangular chocolate bar marked into m × n squares, and you wish to break up the bar into its constituent squares. At each step, you may pick up one piece and break it along any of its marked vertical or horizontal lines. Prove that every method finishes in the same number of steps.

From the author's comments:

This ridiculously easy puzzle has been known to stump some very high-powered mathematicians for as much as a full day, until the light finally dawns amid groans and beatings of heads against walls.


I thought to myself thought I, I am a dude who knows some math, I can figure this out!


Initially I assumed that a proof by induction would be the easiest way to solve the problem.  If we assume that a mxn chocolate bar always finishes in the same number of steps then can we prove that a mx(n+1) chocolate bar does the same?  


I won't be perfectly rigorous here, rather I will just outline the proof.


The mxn bar has a series of breaks that will separate it entirely.  This series of breaks, if performed on the mx(n+1) bar, will leave m pieces that are composed of precisely two squares each.  This means that we would need m additional breaks to completely break the new bar.  If there are some breaks along the line between the new squares and the old squares then for each such break we will separate q squares where q is between 1 and m of the new squares from the original bar.  In this case the q squares can be fully separated by q-1 breaks.  Any number of these breaks can occur but the total number of squares that can be separated in this way is equal to m.  Since each q squares require q breaks to separate regardless of the order of operations then the mx(n+1) bar always breaks in (the number of breaks required for mxn) + m.


Great, so I have a proof that isn't super rigorous but certainly works.  I believe it was Barrel Plug who always told me to try a proof by induction first; you can do an end run around all kinds of tricky problems with induction.  It's like cheating!


Then I began to think about it for real and hit my 'groan and smash head' moment.


So the chocolate bar has 1 piece.  Each time we break it we add 1 to the number of pieces.  We must get m*n pieces, so no matter how we break it we must perform exactly m*n-1 breaks.  Oy.  So this is in fact a truly simple proof that relies on no mathematical training at all but which can be solved in much more complex ways if you want to.


I like this problem.  Easy solution that everyone can understand but which most people will never think of because they approach it the wrong way.