The Jaded Gamer

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Zendo: Total is prime - illegal rule, or just cruel? Plus a bonus game of Zendo to play at home!

Alec Chapman
United Kingdom
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For those who don't know Zendo, I'll run through it quickly:

The box game (and the version I played at LOBStercon) was based around Icehouse pyramids, which are now known as the far less cool sounding "Looney Pyramids".
From these colourful pyramids one player, known as the "master" will build two constructions, known as "koans". One of these Koans conforms to a secret rule known only by the master, the other does not.
The job of the rest of the players is to ascertain the nature of the secret rule by building their own koans and finding out if they have the "buddha nature" or not.

Components note: You can play this with anything that has several characteristics in each piece. Looney Pyramids (I hate that name!) have three possible characteristics on their own (colour, size, orientation) and many more in combination (touching/untouching, stacked/nested, pointing towards each other/away from each other etc).
There is nothing to stop you trying the game for yourself with Lego or even just words (vowels, consonants, number of letters etc)

Questions over the theme aside, it's a great fun exercise in inductive reasoning. Great fun, that is, unless the master decides to be annoying rather than cunning.

One master told us that his rule was horrible but contained just four words. Alarm bells rang for me because I don't think the point of the game is to be horrible... but we went on anyway.

Thing is, Zendo can bog down into misery if you don't know the key, and at one point I got so testy I accused him of coming up with "there is no rule" - sorry about that, I was tired and grumpy!

The rule was, in the end, "The sum is prime" or something like that (to denote size, Looney Icehouse Pyramids have pips from 1 to 3 on them).

Now, in the back of my mind I remember that a prime number is a number that can be only divided by itself and 1 (1 is excluded by convention, despite him marking a koan totalling one as correct), but I am not a mathematician so my knowledge of that is purely trivial. I don't put it on the same intuitive level as, for instance, "odd" and "even" numbers.

It also opens up a can of worms in terms of the rules of the game.

The concept of "prime numbers" is not present in the Koans, while the total values are, and the point of the game is not to reference anything outside of the constructed Koans themselves. Does the concept of prime numbers fit the bill as being present within the Koans?

And I know that the concept of "five" isn't present either, but the pips that total the number five are. Of course, I wouldn't complain about odd and even so I am partially, at least, a hypocrite.

That being said, the rule "the pip total is even" can be expressed as "the pip total is divisible by two into whole numbers"
as opposed to
"the pip total is only divisible into whole numbers by the number one and this same number that the pips total"
which is clearly a far more complicated rule and clearly (imho) outside the spirit if not the letter of the rules.

Again, this is only for people for whom being prime or not is hardly considered a fundamental property of a number - in the same way that not everyone knows the Fibonacci Sequence or a Triangular Number sequence etc. A master should really consider his audience when designing a rule to ensure the experience is satisfying rather than frustrating

Ironically, me and Martin (qwertymartin on BGG) had just joked about this rule as being a ridiculously annoying one while the master was off writing his rule down.

Anyway, self serving rant over - have this little game of Zendo as an apology. You can play along if you want. Simply suggest another word and I will tell you if it has the "Buddha Nature". If you get it right you can guess the rule! (PS this is a gross simplification of the actual rules for the blog, but never mind)

"Involve" has the Buddha Nature
"Indeed" does not have the Buddha Nature
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