I've encountered a numerical quandary which I'm hoping some of the math mavens around here can help me with...

I'm trying to work out an arrangement of numbers on a page as follows. The page is divided into quadrants. It's got a bunch of numbers on it. Either they're all two-digit numbers, or they're all three-digit numbers (I haven't yet worked out which). They're arranged so that the following is possible: You choose any number on the page. You then select one of the digits in that number. (In the two-digit version, you can select either digit; in the three-digit version, you can select either the second or third digit, but not the first.) Whatever digit you've selected, you then find, from anywhere on the page, a new number that begins with that digit. You then repeat the process: pick one of the digits, find a new number that starts with it. The process may be repeated more times, but for explanatory purposes, suppose that's the last time. So you've chosen a total of three different numbers, each of which lies within a given quadrant on the page.

Now suppose you kept track of which quadrant each number came from, in the order in which they were chosen. In other words, say your first number was in Quadrant 2, your second number was in Quadrant 4, and your third number was in Quadrant 1. For want of a better made-up term, I'll refer to this as the Quadrant Order. In this case, the Quadrant Order for the sequence of numbers you chose would be 241.

Now here's the goal: I want to figure out how to arrange the numbers so that any given Quadrant Order could only be generated by one sequence of numbers; in other words, the sequence of numbers you chose is the only sequence that would generate that particular Quadrant Order; in other words, if I knew the Quadrant Order, I would know which numbers you had chosen, and in what order. Fans of Leo Boudreau will see where this is going.

While I suspect that such an arrangement of numbers is possible, I lack the mathematical background to figure it out intuitively, and my attempts at working it out by brute force / trial and error have failed. My hope is that someone with better math chops than mine can help.

So the basic concept is, if you know which quadrants all the numbers came from, you know what the numbers are. Within that concept, here are the variables:

• The numbers can all be two digits, or they can all be three digits, as described above.

• There can be as many or as few numbers as are necessary to yield the desired result, within reason. (Four would be less than impressive; 1024 would make for a mighty big crib sheet.)

• The selection process (pick a digit and find a new number that starts with it) can be repeated as many times as necessary.

• The number of numbers that begin with the same digit is variable, but should at least be greater than one so that the participant has a genuine choice when picking a new number.

• This is the biggie: the numbers don't have to be base 10, but can be anything up to base 26. This is because when I actually put this to use, I won't be using numbers and digits, but rather words and letters. I don't know what the standard is for representing numbers in larger-than-base-10 systems, but in my own scribblings I've been representing, say, a three-digit number consisting of the thirteenth, fourth, and twenty-first digits as [13,4,21]. If there's a better/more accepted way of doing it, feel free to hip me to it.


This is my goal. Anyone who can help me realize it will receive more gratitude than I can express in ASCII.

[Whoops, replied to the wrong post.]

Does the end justify the means? Why not just glean a randomly chosen number via thought transmitter or some other way? Unless, of course you have some other necessary application for it which I am not aware. Just a thought!

Well, here's the effect I have in mind. I hand someone a piece of paper with a bunch of words on it. I ask them to mentally choose a word and conentrate on it. They do. I write something down, but don't show it to anyone yet. Then I ask them to concentrate on one of the letters in the word they're thinking of. I write something again. Then I ask them to choose a new word on the page that starts with the letter they're thinking of. They do. I write again. I ask them to concentrate on one of the letters in this word. I write. I again ask them to choose a new word starting with the letter they're thinking of. I write once more.

At this point I show what I've been writing to the audience, but not to my helper. It says, for example:

You're thinking of DOG.
You've chosen the G.
You're thinking of GET.
You've chosen the E.
You're thinking of ELM.

I then ask my helper if he remembers the first word he chose, and which letter from that word, and so forth. And of course, I've divined his thoughts correctly every time.

In short, the effect is that I divine five (or more, depending on how it shakes out) freely selected thoughts that genuinely exist only in my helper's mind; they're never written down or communicated to anyone else. If I can do that, then yes, for me it will be worth the effort of figuring it out.

Interesting challenge. I found a solution by limiting the choice of letters to either the second or the third letter in the word instead of allowing the volunteer to think of any letter. With this small change, the solution is:

Quad 1: sad, ape, pit, orb
Quad 2: dam, elf, mow, wun(derkind)
Quad 3: low, run, ids, ult(imate)
Quad 4: tad, foe, bun, nit

The volunteer's free selections will produce one of 64 possible codes. Here are a few examples:

111 = sad - a - ape - p - pit
112 = sad - a - ape - e - elf
113 = ape - p - pit - I - ids
114 = ape - p - pit - t - tad
121 = sad - d - dam - a - ape
122 = sad - d - dam - m - mow
.
.
etc.

Incredible.

Folks, in another 15-20 years, when advancements in data capture, translation, and transmission make it impractical to have specs write their thoughts down in any form, Leo Boudreau will be the man we turn to.

Leo, many many thanks. You are the man.

And I am so glad that hardly anyone reads this section...

Very cool.

Quinn,

Mr Boudreau has been the man to turn to for ages when it comes to these things. Would be excellent to combine this with his Murder Most Foul whis is similar.

/Tomas (Long time Boudreau fan)

I don't understand how what Leo wrote does anything to the effect. I understand how it has to do with the effect, but if you write down a prediction and show it to the audience, and only then does the spectator say the words he was thinking of, how does it help?