Each child is sitting in front of a conical beaker roughly four-fifths full of water. A small rubber ball is bobbing on the surface, just out of reach of their fingers.
Scattered around the beaker is an array of possible tools: corks, rubbers, small sticks, scraps of polystyrene and fluff. The boys' task is to extract the balls without tipping the beakers over.
With a bit of practice, most grackles crack the challenge pretty quickly, realising that if they drop enough dense objects in they will eventually raise the water level and displace the target.
My younger son, however, has yet to have his Archimedes moment. He has spent the past 15 minutes cheerfully but indiscriminately prodding at a growing mass of floating objects.
This should not come as a surprise. There is emerging evidence that grackles, alongside a handful of other bird species, possess cognitive skills that children only begin to acquire when they are six or seven.
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Crows, for example, can fashion hooked tools from the stems of plants, share skills with other members of their flock and pass grudges down to their offspring. Some studies even tentatively suggest that they exhibit rudimentary signs of self-consciousness.
My sons, aged six and seven, are precisely at the threshold where corvid or grackle-level reasoning ought to be starting to appear.
This impromptu experiment has been set up by Corina Logan and her husband Dieter Lukas, who are animal behaviour researchers at the Max Planck Institute for Evolutionary Anthropology in Leipzig.
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The fundamental question they are trying to answer is what makes a species capable of suddenly expanding into new territory, just as our ancestors have done several times over the past 100,000 years: persistence? Bravery? Or possibly sheer curiosity?
The great-tailed grackle is an ideal test subject. For millennia the birds' foraging grounds were confined to parts of Central and South America, although the Aztecs introduced them to their capital ,Tenochtitlan, in present-day Mexico City, apparently fascinated by the gorgeous sheen of their feathers.
Then, between 1880 and 2000, their range exploded more than 50-fold in the blink of an evolutionary eye, expanding from the southern fringe of Texas to as far north as the Canadian border, and following corridors of urban and agricultural development.
The grackles clearly had some special trait that allowed them to supercharge their growth as the habitat around them changed, much as ancient humans did.
The latest research by Logan, Lukas and their colleagues, which was published as a provisional pre-print last week, suggests that trait is flexibility: the capacity to adapt behaviour when the rules change.
Strikingly, the team have also found indications that training the birds' flexibility in experimental settings actually makes them better at exploring and foraging in the wild afterwards.
"I didn't think it would actually work, and I'm so shocked and happy that it did," Logan said. "It opens up a whole new world for conservation."
This is why we have visited Logan and Lukas at their home in Leipzig for a child-versus-grackle competition: to test how much birds and young humans share the evolutionarily crucial ability to work out the rules of an unfamiliar game then roll with the punches when those rules are altered.
Once my children have finally discovered how to displace the bobbing rubber balls by dropping dense objects into the water, they are asked to extract rubber bands from a series of puzzle boxes that are almost identical to those tested on the grackles. Sometimes the patterns shift or reverse as soon as the boys identify them.
Ultimately, the children perform close to the upper end of the grackles' scores, especially in challenges where the rules are abruptly twisted.
They have more or less defended the honour of their family and species. This was not a foregone conclusion: adults, Logan says, sometimes struggle with the beaker task, stubbornly pursuing a single strategy even when it is patently not working.
We leave Leipzig feeling a little relieved that our six-year-old is as smart as a bird.