Questions about something-for-nothing schemes turn up frequently in my mail. So many "free offers" are based on myths that a few comments may be in order.

The cents-off coupon and the manufacturer's rebate are now the two most frequently encountered promotion schemes. Both are useually genuine. I recall no instance in which either turned out to be fraudulent.

If a coupon, a label, an imprint on a package, a commercial on radio or TV, or a printed advertisement offer something of value in exchange for "proof of purchase," it's a pretty good bet that the offer is valid.

On the other hand if you hear about a "free offer" by word of mouth but never see or hear it advertised, beware. When an offer is genuine, the company making it will publicize it to increase its effectiveness. If the free offer isn't advertised (at the very least on the product itself), there is a good chance it is a hoax.

Be especially wary of alleged free offers that make no ecobomic sense.

If you see an ad in a veterans' magazine that says a certain cigarette company will donate free cigarettes to hospitalized servicemen in exchange for empty packages of that same brand, you can believe it. That kind of scheme would boost sales for the sponsoring company.

But if you are told that a cigarette company (or any other firm) will give something of value for empty packages of all brands, don't be taken in. Why would any tobacco company be willing to reward you for having bought a competitor's product?

Of especial interest right now is the fact that a few companies have begun to specify that the "proof of purchase" to be submitted to them can be, or must be, the Universal Poroduct Code labels that identify their products.

This development has given new credence to the myth that all coded labels have a value, and that if you and your friends save these labels indiscriminately you can trade them for medical help for a needy child. If you just stop to think about it for a moment you will realize that the story doesn't make economic sense. Don't wast your time on such projects.