I got a request to make my “game” of Human Adding Machine described in a previous post more fun-sounding. I have done that below (if you define “more fun” as “more complicated”). As foreshadowed in that post, my version 2 game does involve bottles of beer, but it still does not require partial nudity or body painting (unlike Human Chess).
Caveats. To play this game, someone in the group needs to understand base-7 arithmetic (here is some info on it). It isn’t necessary for the players of the game to understand base-7 arithmetic, or even know that the game is performing arithmetic.
To read the blog post you are reading now, however, and have it sound like fun (my original task), the reader has to have at least an interest in other-base arithmetic, or an equivalent amount of math-geekiness in other areas. You’ve been warned.
Note in press. Shortly after publishing this, my learned friend Pete Boundy correctly pointed out that the H.A.M. game would be 16⅔% more fun if it used base‑7 arithmetic instead of base‑6 as originally written. So this post is a base‑7 revision of what I originally posted.
Players.
One player is called the User. He or she sets into motion the transfer of beer between players.
The other players, called Players, make up the components of the adding machine. The game can have any number of Players, although the more Players you have, the more beer you need.
One person (who can be the User, or one of the Players, or someone else) is the Judge. The Judge’s job is to decide on the addition problem to be solved, and adjudicate at the end whether it was solved correctly. The Judge needs to be able to understand base-7 arithmetic.
Initial setup.
The Judge determines a base-7 addition problem to solve,
for example, 1524(7) + 653(7) = ?
The Players line up, and the Player at the far right of the line is called “Player 1”. Each Player receives a six-pack of beer from the User. The six-pack can have any number of beer bottles in it from zero to six, determined by the User.
Rules of Game play: Players.
1. Each Player can only receive more beer from the User, or from the Player on his or her immediate right.
2. Each Player can only give beer to the person on his or her immediate left.
3. Each Player can receive only one new beer at a time. When a beer is received, it is put in the Player’s six-pack.
4. A Player can receive a beer at any time, but a Player can only give away a bottle if rule 5 applies.
5. If at any time a Player receives a beer and can’t put it in his or her six-pack because it’s already full, all of his or her beer is forfeit. He or she must immediately (a) give the bottle of beer just received to the Player on the immediate left, and (b) take all the bottles of beer out of the six-pack and recycle them, and be left with an empty six pack.
Rules of Game play: User.
1. The User is given the two numbers making up the addition problem, 1524 and 653 in our example.
2. The User sets the initial conditions by giving out six-packs to the Players based on the first number, say 1524. “Player 1” gets a six-pack with 4 bottles in it to correspond to the right-most digit, 4. The next Player over gets a six-pack with 2 bottles, the next a six-pack with 5 bottles, and the next a six-pack with 1 bottle. Any further Players get empty six-packs with zero bottles. (If you have many Players getting zero beer bottles, and you have enough beer, you should pick a bigger starting number to maximize the fun–having no beer isn’t that much fun)
3. Once the initial conditions are set, game play begins. The User starts handing out beer to Players, one beer at a time, based on the second number of his or her addition problem. If the number is 653, the User gives 3 bottles of beer to “Player 1”. The User gives the next Player 5 bottles of beer, because 5 is the next digit. The next Player gets 6 bottles, and the Players beyond that get no bottles in this example.
Note 1. If a Player needs to give away beer, you should give him or her a chance to do that before giving him or her any more beer.
Note 2. there is no required order for the User to give out the beer, as long as he or she gets the totals right. One could give one beer to the first Player, two to the second, then go back and give another to the first before giving some to the third, etc.
4. When the User has handed out all the beer corresponding to the second addition term, his or her role in passing out beer is complete (unless you’re playing Extreme Human Adding Machine, in which more than two numbers are summed!)
5. After all the Players have done all the allowed moves that they can, the game is over. The User then counts the number of beer bottles in each six-pack and converts it to a number: the count of bottles in “Player 1″s six-pack is the right-most (units) digit of that number, the next Player’s bottle count is the next-left digit, and so on.
How to win.
VARIATION 1: The User generates a number from the final distribution of beer bottles as above. The Judge determines if this number is the correct answer to the addition problem.
In the example used above, 1524(7) + 653(7) = 2510(7).
If the addition was performed correctly, everyone wins! and all drink beer. If the answer is incorrect, everyone loses, and all drink beer (but unhappily).
VARIATION 2: In this case, all of the rules of the game are the same, but the object of the game is to maximize your own personal beer supply. So the Player with the most beer in his or her six-pack when the game ends wins, and gets to drink more beer than the losers.
Note that in variation 2, winning the game has nothing to do with whether the addition problem was solved correctly. But because the Players really have no choices to make during the entire game, the problem should be solved correctly anyway. Unless a Player cheats! (Which is exactly what has happened when a computer program you wrote does not run as it should.)
In both variations, the Players don’t need to know or care that they are solving a math problem for the addition to work, just like the little nanogates or quantum wells or whatever they make computers out of these days don’t know they are doing math for you when you run your computer.
Thanks, and sorry!
-Dorn
6/30/19
