The Blog

Put on your thinking caps, katz’n’kittenz. Here comes a word problem!
[UPDATE: My solution appears in the comments below.]

Molly the Cat and Tigger live here in our house. They each came to live with us at different times, and of their own choosing. Those could be long stories, one of which I’ve already told here, so I’ll skip ahead to the math problem.

No sooner had they moved in than they started asking for food. Regular meals, and they were quite insistent about it. Being the good ex-hippies that we are, we took it upon ourselves to provide not just a tasty menu, but also excellent nutrition. It took a while, but we finally found a brand of canned food that they liked and that we thought was good for them, and no less than three brands of dry food (hereafter called “crunchies”).

Tigger is a boy, and a little bigger than Molly, and over time we figured out that he needed more food than Molly. No doubt he thought we were hopelessly stupid during the months it took us to come to this realization, but eventually we did, and here is how the daily diet eventually took shape: Breakfast is at 7:00 AM and dinner (“supper” to you Eastern seaboarders) is at 6:00 PM. At each seating, Molly gets one fifth of a can and Tigger gets one fourth of a can. Throughout the day and in the evenings both of them get all the crunchies they want. To make it easier to measure the fractions of cans, each critter eats only from his or her own can until it is empty, then moves on to the next can in the cupboard. So it takes four meals (or two days) for Tigger to empty his can, and five meals (or two and a half days) for Molly to do the same.

You wouldn’t think that both cans would be empty at the same time very often, would you? You’d be right. But for a long time I have had the feeling that that event (two cans empty at the same time — two fresh cans opened for the same meal) was happening a little too often. For about a year, I had that feeling. Somebody — either me or Mrs. Jones — was screwing up the measurements at feeding time. To be fair, it’s pretty hard to eyeball a fifth of a can, and both of us may have muffed it from time to time.

Last night we figured out exactly how often this should happen. I’m embarrassed to say that it took two college graduates a half hour to come up with the definitive answer, and even now we don’t understand it mathematically. How fast can you solve the problem?

Start with two full cans. Give Molly a fifth of her can at each meal, and Tigger a fourth of his can at each meal. Put plastic caps on them and refrigerate between meals. Whenever a can is empty, open a new one. How many days before you find yourself opening two new cans at the same time?

Go ahead and tell me the answer in the comments, if you can. We figured it out basically by running a model scenario all the way to the end, but there is also a mathematical formula that is much more elegant and sophisticated. Except I can’t figure it out and explain the “why” of it. So help me with that, too.

My answer will be posted soon.

I can’t believe I have all this stuff.

There was a time when owning all of it was just a dream. Now I am standing in my patio at three in the morning, and here it all is, staged between the garage and the house, waiting to be carried inside: A sweet all-tube Fender guitar amplifier, two fancy-assed electric guitars, a rack full of electronics, a couple of duffel bags full of electronic gizmos, miscellaneous adapters, microphones and cables. I lusted after most of this stuff the way some men pursue women, and now it’s just heavy equipment that I have to carry in the middle of the night, and put it somewhere secure, if such a place exists.

I had packed it up and loaded it earlier in the afternoon, hauled it to the bar where I was playing, unloaded it there, unpacked and set it up. Later, we broke it all down, packed it up again, loaded the cars, the truck and the van and brought it back, each of us, to our various homes, and now I was half way through the job of dragging it out of the car and into the house. That’s four times in one day. And did I mention there’s a whole PA system, too, with six speaker cabinets and heavy power amplifiers? Well, there is.

The band sounded kind of good this night. We have bumbled our way into a few gigs, and the extra playing time has sharpened our performance. I find myself turning to look in surprise and delight at the other guys when something, a transition or an ending or a complicated harmony happens just the way we’d rehearsed it.

The people are kind. They say “You guys are great!” They whistle and clap. Of course, they came to have a good time, they are all high in various ways, and they will enjoy themselves, no matter what we do.

But it’s not really a great band. No matter how hard we try, how long we practice, there is a frontier of “greatness” out there beyond the horizon, and really, we are just playing around the neighborhood, staying close to home, keeping our day jobs, our paychecks and medical insurance. Greatness demands a bigger commitment.

I complain privately about the flaws and the failings, but what we are doing is, we’re having great big rock’n’roll fun. At least I am. For those few hours when we’re on stage I’m as happy as I ever get. I stopped playing for money decades ago and only recently took it up again. But my attitude now is “I don’t need the money. I just want it to be offered.” Playing rock’n’roll with this band, any band, for real live people who are dancing and partying — I’d do that for free.

Moving all this equipment — that’s what I get paid for.

I know what it’s like to have something creative inside and not be able to get it out.

Something like a song, a play, a sculpture, a comedy routine, a story.

You know it’s in there, you think maybe it’s “good,” you don’t know how good, but you know you’ve got it. You nurture it inside and it becomes who you are, secretly. You show a little of it sometimes, and that leads to your family and all your friends saying things like “That’s as good as anything on Broadway/TV/the radio/CD’s. You should write/sing/perform more. Go for it!!”

You’re momentarily flattered, but after all it’s your family and friends and they are obviously (and rightly) biased and might not be telling you the truth and they might not be qualified to judge such things anyway, so of course you don’t go for it, because you have to clean the garage, take out the garbage, work for a living (or find a job), get some food, score some drugs, find someone who’ll do you, and so on. There’s no TIME.

But there is time, and time goes on, and one day you look around and half your friends are drifting away in one way or another, and among the other half, half don’t want to know you any more and the other half are dead or as good as, and how long do you think you have remaining to produce anything worthwhile? You don’t know, so you promise yourself you’re going to buckle down and do something, create something while you’ve still got a chance, and by now you don’t even care if anybody likes it or if it gets on Broadway/TV/the radio/CD’s, because it’s like you’ve been pregnant longer than an elephant and it’s about god damned time for the blessed event!

You know what I mean?