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A short story about two Earth engineers who are shown a fake perpetual motion machine and challenged by aliens to duplicate it to prove whether Earth engineers are better than alien engineers.

They succeed, but find that the original machine is fake.

They learn that Earth pulled a similar trick on the alien engineers, showing them a fake antigravity machine.

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    Hi, welcome to SF&F. When and where did you read this? There's a very similar story where scientists are shown a fake antigravity machine and succeed in creating one; is is possible you're conflating stories? (The story is "Noise Level" by Raymond F. Jones as per this previous question.)
    – DavidW
    Apr 23 at 19:35
  • @user14111 Fair enough, except I didn't know the Silverberg story. (It looks like it was thinly collected, and not since 1981, and I just missed it.)
    – DavidW
    Apr 23 at 23:26
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    If the question has been answered to your satisfaction, you can "accept" an answer by clicking on the check mark next to it.
    – user14111
    Apr 23 at 23:48

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"Double Dare", a short story by Robert Silverberg first published in Galaxy Science Fiction, November 1956; you may have read it in one of these compilations. You can read it at the Internet Archive or listen to the X-Minus One radio adaptation.

Summary from Majipoor.com:

When an alien from Domerang V offhandedly remarks that Earth possesses "second rate technology" a dangerous bet is born. Two Domerangi engineers come to Earth, where they will be given challenges to overcome, and two human engineers will go to Domerang for testing. The winners get the prestige of being proven the best. But is there something more going on?

Excerpt: Earthian engineers challenged to duplicate fake perpetual motion machine.

"What is it?" Marner asked.

"You'll see," promised the alien. He fumbled in the back of the machine, drew forth a cord and plugged it into a wall socket. A small tube in the heart of the machine glowed cherry red and the pistons began to move, first slowly, then more rapidly. After a while, it was humming away at an even, steady clip, pistons barreling back and forth in purposeless but inexorable motion. Kemridge bent and peered as close to the workings of the gadget as he dared. "It's an engine. What of it?"

"It's a very special kind of engine," Plorvash said. "Suppose you take the plug out."

The Earthman worked the plug from its socket and looked at the machine. Then the plug dropped from his limp hand and skittered to the floor.

"It—doesn't stop going, does it?" Kemridge asked quietly. "The pistons keep on moving."

"This is our power source," Plorvash said smugly. "We use them in vehicles and other such things. It's the third problem."

Excerpt: alien engineers challenged to duplicate fake antigravity machine.

The old diplomat smiled his apologies. "I hate to admit this, but it seems the people at the Earth end of this deal had much the same idea the Domerangi did."

"Perpetual motion, you mean?"

"Not quite," Culbertson said. "They rigged up a phony antigravity machine and told the Domerangi to duplicate it, just as was done here. Our psychologies must be similar."

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