A READER HAS asked me to help him with a problem he has. The question he posed is: "I notice that PLO leader Yasser Afafat and new Iranian Prime Minister Rajai always manage to appear with a four-to six-day growth of beard, which never grows any longer. How do they manage to do it?"

In order to get the answer I called a friend of mine at the CIA who was very upset that I was on to something. He agreed to meet me in a safe house in McLean, Va. He told me to take a taxi to National Airport, buy a ticket to Bangor, Me., and then at the last moment rent a car and drive to the address.

When I met him at the house there were three CIA agents in the living room who refused to give their names, and my friend.

"Why are you interested in Arafat and Rajai's shaving problems?" one of them wanted to know.

I played dumb. "Just curiosity. A reader asked me and I thought he deserved an answer."

"A likely story," one of the others sneered. "You were tipped off by someone in the agency, weren't you?"

"I don't think I have to answer that."

"We've been working on this problem for months now. There are only six people in 'The Company,' not including the CIA barber, who know what we've been up to. Now it looks as if one of them is a mole."

"You mean he's working for both sides?"

"It's obvious he is. To get to the bottom of this, we'll tell you what we know if you tell us what you know."

"It sounds good to me," I said. "It seems there are a lot of leaders in the Middle East who don't shave every day. By the same token they refuse to grow beards. They prefer a four-to six-day growth, but no more. My source believes they're all using the same razor blade."

One of the CIA men was taking notes. "He's on the right track," he said.

"Did your source tell you how they manage to get the razor blade back and forth?"

"Arafat seems to be the bag man. He's always traveling somewhere and my man believes he has the razor blade hidden in his turban. We've never seen a picture of Yasser without his headdress. It would be the obvious place to keep it."

The men looked at each other before one spoke.

"Suppose we told you it wasn't a razor blade, but a Soviet electric razor."

I hit my head with the palm of my hand. "An electric razor. I never thought of that. But wouldn't an electric razor give them all a clean shave?"

"You would think so," my friend said. "But we have evidence that the Soviets have been unloading bum electric razors on their clients in the Middle East. No one in Russia will buy them because they will hardly cut any kind of beard, so every time a leftist leader comes to Moscow they give him one as a gift. Arafat shaves every day with one, and so does Rajai and a lot of the other people in that part of the world. But even on the adjustable high setting it's the best they can do."

"Why do you people want to keep this a secret?" I asked. "I should think it would be to our advantage to publicize the fact that the Soviets are unloading rejected electric razors on their friends."

"Because every morning when Arafat and his cronies shave it causes them excruciating pain, and for the moment we want to keep it that way."