*Remember the old cartoon? A professor stands by the blackboard as his student chalks out a complex formula. Right in the center of this mathematical masterpiece is a gap, in which the kid has written “AND THEN A MIRACLE OCCURS.” *

Yesterday, Ray revealed the answer to his “Prisoners and Light Switches” puzzler of two weeks ago. My family and I listened with keen interest, having already firmly established for ourselves that **there is no solution to this puzzler**.

It seems other listeners (if any) thought similarly, thus crickets were clearly heard in the Puzzler Tower mail room.

At that sensitive juncture, Ray did unfortunately sidestep his sworn duty and obligation to announce the answer (and receive the inevitable rotten tomatoes). Perhaps some may feel he chickened out; I don’t think so at all. I’m sure he’d simply realized there was a LOT of work to do on LAST week’s puzzler, and he meant to get right down to it!

Quick to fill a looming gap in the show, Ray also stepped up with some powerhouse misdirection. He suggested we could ignore his previous misdirection such as the prologue about Hungarian mathematicians; it’s just a simple old puzzler! “A 6th-grader could do it”, he assured us, and maybe we poor idiots who hadn’t yet figured it out should “try with three prisoners instead of 23” (if you do, you’ll see it still doesn’t work). Tommy got into the act by exclaiming these inmates have life sentences (uh, not last week they didn’t), then casually mentioning that 23’s status as a prime number is irrelevant to the problem. (He’s right. Three being a prime number is also irrelevant. Both of them being ODD numbers is downright kind, but this puzzler needs wayyy more help than that!)

Thus were we gifted with a nice extra spot of time to cudgel our brains some more over this thing, just in case we’d missed some arcane tidbit or ray of hope in what seemed to be a pretty straightforward insoluble math problem.

So, HA! Fast forward through the cruel and unusual two-week wait, and we’re rewarded with “the Answer,” and here it is:

**One prisoner will act as the “counter” (let’s call him Carlo) who will visit the switch room 44 times, track the switch position changes made by the other 22 prisoners according to instructions, and conclude that all have visited the room at least once. Carlo tells the Warden, who frees our happy inmates! **

… but …

Um, one of the stated variables in this puzzler is that the Warden will bring prisoners in randomly: maybe he’ll pick one guy three times in a row, and/or he could have two inmates alternating visits for a week before moving on to others, and so on.

First, let’s review what the Warden says we can count on:

- Each of the 23 prisoners must move one switch, but never two switches.
- Each prisoner will visit the room.
- Each will visit the same number of times as any other prisoner. Eventually.

And then the variables - a.k.a. UNKNOWNS - in this Warden’s rather diabolical riddle:

(1) Initial position of switches,

(2) Number of each prisoner’s visits,

(3) Order of visits,

(4) Time between visits, and

(5) Time span for all visits (a.k.a. Eventuality).

PROBLEM: *Ensure that Carlo gets at least one switch room trip after his pals have all visited.*

SOLUTION: {Empty Field!} *No idea! What’s he supposed to do, wear lame’ and sing “save the last dance for me” every time the Warden strolls by??*

Even with the assistance of a really clever 6th-grader, there’s no way to predict or control Carlo’s place in the Warden-designed series of prisoner visits to the switch room. He might be brought there four times early on (with or without other prisoner visits interspersed with his), then never see the room again as the other inmates proceed to complete their own visits while Carlo sits in growing dread that he’s somehow missed the signal…

OK, let’s work with it for a moment. We’ll hypothesize that Carlo gets unbelievably lucky and is called to the switch room 44 times AND kept good books on the switch signal AND has seen the right signal come up AND is about to turn to the Warden and open his mouth.

… but, but…

We were also told that eventually, all prisoners will have visited the switch room an equal number of times!

PROBLEM: *How does Carlo determine that each prisoner has visited an equal number of times? And does he have to? And… how long is “eventually?”*

SOLUTION: {Empty Field!} *Oh, come on! After eight or ten visits by each inmate, the Warden might tire of his little game, give up, and go back to golf. Even if we posit endless Warden patience with the process, most of the inmates will be either released or dead of old age by the time the math dice roll up on a Carlo-verifiable equal number of visits!*

Sorry, Ray! That answer ain’t makin’ it unless you want to go back to it yet again & add a constant or two to the mix (like, Divine Intervention)!

**Real Answer? Only the Warden knows for sure. Even IF THE NUMBER IS TWO, Carlo’s life is about to get harder. His sentence will be served and he’ll be out in the world looking over his shoulder for those ex-con buddies a little sore at him for not doing the job he was supposed to do for them! **

Just a thought!

*BETTER LUCK NEXT WEEK, GUYS!!*