Why Are There So Many Bats At Spurs Games?

There are a few things we’ve come to expect over the years from San Antonio Spurs basketball. The team will always find a way to make the playoffs, no matter how much talent and pedigree it loses during the offseason. Coach Gregg Popovich will generally deliver grumpy end-of-quarter interviews no matter how well his team is playing. And once in a while, we can expect a furry, winged menace to descend from the rafters and terrorize their home court.

The local bats of San Antonio have long held a reputation as unruly Spurs fans, occasionally crashing games and disrupting play. In recent weeks, though, the bats have claimed season-ticket holder status with the red-hot team, which has won six-straight contests. In three of the team’s past six home games, including this past Sunday, one of the flying mammals has brought a Spurs’ game to a screeching halt for minutes at a time, as various team staffers furiously scrambled to apprehend the flapping intruders.

All of which raises the obvious question: Why is the arena plagued with bats so often?

After spending many sleepless nights investigating the matter — in truth, I just called a couple of local specialists — the answer actually makes pretty good sense. The AT&T Center is 25 miles southwest of Bracken Cave, which is home to more than 15 million Mexican free-tailed bats, making it the largest summer bat colony in the world.4

What’s more, it’s logical that bats would fly past the arena, particularly during the winter months. The stadium is almost directly in the bats’ migration path from Central America and Mexico back to Bracken Cave, where maternal colonies fly to have and nurse their newborns (nearly doubling in number).

Still, the team’s proximity to the real-life Batcave alone doesn’t explain how the bats are working their way inside the venue.

There are a couple of potential factors at play. First, the San Antonio arena — a few miles outside of the city’s downtown area and adjacent to a golf course — is perhaps the closest thing to a suburban venue in the entire NBA. The massive, brightly illuminated presence that attracts moths and other insects in an otherwise quiet area might be appealing to bats5 that are looking for food on a given night, according to Judit Green, who has worked as an urban wildlife biologist for 30 years with the Texas Parks and Wildlife Department.

Beyond that, experts suggest that the 750,000 square-foot stadium almost certainly had — or potentially still has — a tiny crevice somewhere, releasing just enough warmth outside to entice bats and birds that are looking to escape the area’s colder-than-usual temperatures for a night. (The Spurs declined to comment or to make a facilities specialist available to be interviewed for this story.)

“I’d guess there’s a small vent or other opening to the outside that’s attracting the attention of migratory bats,” said Merlin Tuttle, an Austin-based ecologist who has studied bats for 60 years and founded Bat Conservation International in the 1980s. “When cold fronts hit, sometimes that’ll drive the bats wintering in San Antonio to look for a place that gets them out of the cold.”

Once a bat does make it into the arena, we’ve seen time and time again what type of hilarity may ensue. It was nearly a decade ago in 2009 — on Halloween, fittingly enough — that future Hall of Famer Manu Ginobili endeared himself to Spurs’ fans even more by swatting a disruptive bat out of the air with his bare hand.

To be clear, the AT&T Center isn’t alone in producing odd animal-related headlines. It’s nothing new for pro sports, particularly ones played outdoors, to be interrupted by uninvited animals like squirrels, cats, birds, bugs, dogs and rabbits, just to name a few. And bats have also popped up once each this year at NBA games in Utah and Indiana, respectively.

But the San Antonio arena has developed a reputation for general weirdness over the years. Aside from a pigeon that flew overhead at the arena in early January, a snake was found in the visiting locker room before a playoff game between the Blazers and Spurs in May 2014. A month later, during Game 1 of the NBA Finals, the air conditioning stopped working — a development that became controversial after visiting star LeBron James cramped, shifting the momentum of the contest away from Miami and toward San Antonio. The Spurs went on to dominate the series, and James left the Heat the following month in free agency.

While the team did hire a designated pest-control expert following the Ginobli incident, the little-desired task of removing the bats usually falls to arena staffers who just happen to be on the court — and needless to say, it doesn’t always go so well. A handful of Spurs’ employees often give unsuccessful chase to bats, usually armed with nothing more than towels. Even Coyote, the team mascot, has gotten in on it — and, in a few cases, has actually been the one to round up the bats, illustrating just how much of an all-hands-on-deck process it can be.

Rob Wicall, who served as the mascot for nearly two decades before stepping down in 2016, sounded almost envious of all the bat run-ins there have been lately. For years, well before Ginobili’s bat-swat back in 2009, Wicall kept a fishing net he’d bought and the mascot’s Batman costume accessories nearby,6 just in case a bat ever got loose in the arena.

Ginobili took care of the problem just before Wicall could suit-up and come to the rescue back in 2009. But during his farewell season, Wicall got another chance to be the hero before a game in December 2015, and he made it count. He couldn’t see that well — the costume allows little to no peripheral vision — but he tracked the bat into the painted area before somehow nabbing it with his net. When he realized he’d succeeded, Wicall — in Coyote’s full Batman attire, with the PA announcer playing the old-school Batman theme song over the speakers — lifted his arms triumphantly.

“It was one of those bucket-list things for a mascot, because you’ve not only solved a problem in the arena, but you’ve also brought entertainment,” said Wicall, adding that it took him less than 45 seconds total to dash into his changing area and throw on Coyote’s Batman accessories.

But not everyone relishes these run-ins. Spurs forward Rudy Gay sought shelter from a bat by hiding behind ref Zach Zarba last month. And Nets All-Star guard D’Angelo Russell, who has now had two separate bat experiences at AT&T Center the past three seasons, took refuge in the tunnel leading to the locker room as four bats circled over the court.

Bucks center Brook Lopez, on the other hand, would activate a Bat Signal if he could. As a comic-book aficionado, Lopez told SB Nation early in February that he’d welcome being bitten by a bat in hopes that it might make him a superhero.

“I’m just going to make myself available [to the bat],” Lopez said. “At that point, it’s up to the bat. A lot of it is up to fate in these superhero stories. But I want to give myself a shot.”

Fate seemed to be listening. A bat flew past Lopez on Saturday in San Antonio. Fortunately — or perhaps unfortunately, given Lopez’s hope of becoming a superhero — he wasn’t bitten.


What Happens When Humans Fall In Love With An Invasive Species

On a rocky strip of Lake Superior beachfront, the rites of spring begin at dusk and involve fish. Lots and lots of fish. Every year, like clockwork, slender, silvery rainbow smelt, each no longer than your hand, return from deeper waters. They arrive just as the crust of winter ice on the water breaks apart, looking to spawn in the frigid creeks that run out of the hills north of Duluth, Minnesota. For three or four nights, maybe a week if you’re lucky, thousands of smelt jostle their way out of the lake.

And that’s where the humans are waiting.

On this night in early May, on the narrow mouth of the Lester River, there are only about a couple dozen people present. They stand around, bundled in hooded sweatshirts layered under thick rubber overalls that cover their bodies from toe to nipple. The smelt have not yet arrived and the beach is quiet. Waves lap the shore. Someone kicks a rock.

But 40 years ago, smelt fishing on the Lester River was something else entirely. “There were people all over the place, bumper to bumper on London Road,” said Don Schreiner, fisheries specialist with the Minnesota Sea Grant. These now-tranquil shores were once home to a circus tent that housed an all-night smelt fry and a party atmosphere so wild that Schreiner’s parents wouldn’t even take him and his siblings down to the beach. In addition to hangovers, the smelt also brought a tourism industry. There were professional fishermen catching and selling smelt. It was a huge cultural event. “And then,” Schreiner said. “It crashed.”

Starting around 1979, smelt numbers in Lake Superior plummeted. In ’78, commercial fishing companies took in nearly 1.5 million pounds of smelt. A decade later, the haul was 182,000 pounds. There is no commercial smelt fishing on Lake Superior today. But because the smelt in Lake Superior are an invasive species, their decline is actually a sign that the lake is becoming healthier, ecologically speaking. From a cultural and economic perspective, though, the North Shore isn’t what it was. So is the decline of smelt something to celebrate? And if so, who should be throwing the party?

Some people miss the glory days of Lester River fishing even when evidence suggests that Lake Superior and the people who rely on it are better off now. Facts, it turns out, can’t always sway emotion or reshape business plans. And these issues are not unique to smelt. All over the world, you’ll find invasive species that are beloved by humans — even as these foreign plants and animals alter or damage the environment. The fight against invasive species is often framed as a technological problemhow do you selectively eliminate a species once it’s made itself at home in an environment? But in reality, it’s also a question of human hearts and minds. And those might be the harder obstacle to clear.

Smelt may not fit into the stereotype that invasive species are all bad, but the sea lamprey does. Snake-like fish that suck the blood of other animals, lamprey were devastating to the Great Lakes, all but wiping out populations of native trout. At the same time, native herring populations were also declining, and lamprey may have had a hand in that, too, Schreiner said. The lamprey’s swath of destruction cleared the way for smelt, whose populations grew as they filled the gaps those native species left behind.

In the world of invasive species, sea lamprey are, arguably, public enemy No. 1 — the toothy alien maw grinning from a wanted poster.

But while the lamprey and smelt are connected, they affect the environment very differently. In the world of invasive species, sea lamprey are, arguably, public enemy No. 1 — the toothy alien maw grinning from a wanted poster. Nobody loves a sea lamprey. They kill native fish. They are neither beautiful nor delicious.9 They put commercial fishermen out of work. The story of the lamprey is the story of a clear villain that the good guys can (at least try to) vanquish. A poison designed to kill lamprey, and only lamprey, has helped drop the population from nearly 800,000 to around 100,000 in Lake Superior.

That’s the narrative about invasive species that you’re most likely to hear. Whether it’s kudzu engulfing Southern forests, emerald ash borers wiping out the tree canopy in whole cities, or the beaver-like nutria devouring Louisiana like a swamp buffet, the prototypical invasive species story doesn’t leave a lot of room for the color gray.

A half-hour of fishing nearly fills a 10-gallon bucket with rainbow smelt. On a few nights in early spring, thousands of these invasive (and delicious) fish swim en masse from the deep waters of Lake Superior and into coastal streams.

But smelt are more complicated — which is to say they have more redeeming characteristics. Take, for instance, their relationship with lake trout. Smelt numbers exploded as wild lake trout declined in the 1950s and ’60s. Around the time Don Schreiner’s parents were refusing to take him to late-night fishing parties, commercial fisheries on Lake Superior were bringing in millions of pounds of smelt a year. For the trout that remained, those smelt became a crucial food source, as other, native food supplies were lost. In 1986, smelt accounted for 80 percent of a Lake Superior trout’s diet. Decades later, smelt are still a major food source for trout, even as the smelt themselves may be partly responsible for the shrinking numbers of the trout’s native food source — herring. Smelt also form the basis of the diet of the Lake Superior salmon, another species that came to the lake from somewhere else. The salmon are a mostly self-sustaining population now, but even though they’re not native to the lake, no state government is making an effort being made to eradicate them, Schreiner said, because, well, many people enjoy fishing for salmon.10

All of this produces a rat’s nest of competing interests and emotions. The people who I met fishing on the Lester River want smelt to stick around so they can share a tradition (and a meal) with their children and grandchildren. Steve Dahl, an independent commercial fisherman I interviewed, wanted the smelt gone because they interfered with his herring business. Schreiner sees smelt as a useful, if maybe not ideal, food source that now plays a role in the ecosystem of the lake. And he remembered that in 2005, as Minnesota’s Department of Natural Resources was making long-term plans for managing wildlife in the lake, some people who like to fish for salmon tried to convince the department to start adding more smelt to the lake in hopes of producing more salmon. Even if some people really did want the smelt gone, pretty much everyone I spoke to agreed there’s no clear means of killing the species off.

Turns out, this kind of nuanced story is the norm in the world of invasive species. It’s the sea lamprey — clear villains — that are the exception. In Lake Superior in 2017, for instance, the National Oceanic and Atmospheric Administration counted 82 non-native species, only about a quarter of which were harmful invasive species that provided no redeeming benefits.

Globally, nobody knows exactly how many invasive species have muscled their way into spaces where nature didn’t intend them to go, or what percentage of those species are smelt-like mixed bags vs. lamprey-like forces of pure destruction. Instead, invasion biologists have synthesized decades of research into a simple rule of thumb. Of all the species introduced to new environments, we can assume that about 10 percent will successfully start breeding and living on their own. Of those, about 10 percent will become truly harmful. In other words, 1 percent of all non-native species will end up seriously harming their new homes. We don’t know everything, said Marc Cadotte, professor of urban forest conservation and biology at the University of Toronto, Scarborough. But “we do know it is a small minority of species that end up becoming serious problems.”

Technically speaking, smelt are not an invasive species. Instead, they are classified as a non-native species, a larger category of which invasive species are just a subset. According to a 1999 executive order that established the National Invasive Species Council, an invasive species is a non-native plant or animal “whose introduction does or is likely to cause … harm.” But what counts as “harm”?

The answer to that question is supposed to show us how to cut through the knots of competing interests and decide how to allocate scarce resources for the management of invasive species. But “harm” is also basically impossible to define objectively. An ecologist might see harm as altering the function of the natural ecosystem or reducing the populations of native species, Cadotte said. While someone else, looking at the same situation but focused on economic impacts and recreation, might not see the harms that worry the ecologist. It’s very common to have a plant or animal seem obviously harmful to one group of people and obviously benign to another. Take cats. “Cats are introduced all over the world. They have massive impacts on native songbird populations. But nobody in their right mind would classify them as invasive and try to control them,” Cadotte said. “I mean, except Australia.”

There are plenty of other examples. Take those salmon introduced to Lake Superior and prized by many sport fishermen. The state of Minnesota regulates the size and quantity of salmon you can catch, which helps keep their numbers stable. The Grand Portage Band of Lake Superior Chippewa, on the other hand, treats salmon as an invasive species that it wants gone. There’s no limit on how many of the fish tribal members can catch. In the past, the tribe has actually killed non-native sport fish in its streams in order to more effectively stock those streams with native trout, said Seth Moore, director of biology and environment for the Grand Portage band.

Another example: The earthworms that live in the soil along the shores of Lake Superior are invaders from Europe, and while they’re great for gardens, they alter soil quality in forests and make those ecosystems less hospitable to native plants, said Stuart Reitz, professor of entomology at Oregon State University. In other parts of the country, beekeepers and ranchers have fought bitterly over whether an invasive flower, called yellow starthistle, should be considered generally beneficial (because it is to bees) or generally harmful (because it is to livestock), said Mark Hoddle, director of the Center for Invasive Species Research at the University of California, Riverside.

This isn’t just trivia. Invasive species control is always expensive, and you only get the resources to launch a full-court press against a plant or animal — like the hundreds of millions of dollars spent in the last six decades to get sea lamprey populations under control — on the rare and shining occasion when everyone in power agrees on what “harm” is. And so the definition of invasive species has also created fights within the biological sciences. In 2011, Mark Davis, a biology professor at Minnesota’s Macalester College, published an essay in Nature in which he and 18 co-authors argued that the field of invasion biology had become too weighted toward viewing all non-native species as bad and worthy of eradication. “Harm,” he argued, had come to mean “change.” “And, boy, this world is a bad place to be if any change is viewed as bad,” Davis told me.

But other biologists have pushed back against Davis. Some, like Daniel Simberloff, professor of environmental science at the University of Tennessee, Knoxville, really are suspicious of the idea that an ecosystem changed by non-native species is something that could be neutral or balanced, let alone good. “A parking lot [still counts as] an ecosystem,” he pointed out. But even if this new ecosystem is healthy in its own way, that doesn’t mean it’s a good replacement for the forest that once occupied that land.

Most of the scientists I spoke to, however, had not drawn such hard lines in their views. Non-native incursions could be neutral — or, at least, not bad enough that they needed to be prioritized for eradication. The basic idea was that we should try to stop new invasive species, and when something is really damaging, we should invest in serious eradication efforts, but some non-native species just aren’t worth spending the energy and cash required to get rid of them. Smelt, in this conception, are a non-native species, not an invasive one. They’re here now, and we have to deal with them. “You have to dance with the one what brung ya,” said Marc Gaden, communications director for the Great Lakes Fisheries Commission. “Manage with the reality that’s out there.”

But that could be changing. In the future, it might be easier to wage a lamprey-esque war against a smelt-esque species.

Invasive species management is a small-government sort of problem. The federal government can contribute in some ways, particularly by seizing unwanted flora and fauna during customs checks, but most choices about which species to accept and which to fight are being made at the level of the states … and counties … and cities … and even on the level of individual private parks and reserves. Eradication campaigns are complex and expensive, so usually a lot of people have to agree about that a species is harmful before it gets marked for death. But technology is changing both the costs and the stakes. In a few years, it could be a lot easier and cheaper to stage a successful eradication campaign, Simberloff said.

“We’re getting to the point with the technology where we need to have these conversations for the first time. Do we want a world of gardens, or something wild and dangerous?”

There are a variety of biological controls that scientists may be able to use in the future to produce animals that can’t effectively maintain their own population, reducing a species’ numbers not by killing off existing members but by blocking the next generation from breeding. For example, researchers are working on mosquitoes that are genetically engineered to die off before maturity. And rats whose genome has been altered so that all their offspring are infertile. And fish bred so that all their offspring are male. Simberloff sees that as mostly a good thing — a way to empower governments and communities to protect native ecosystems at a lower cost. A way, more to the point, of pushing back against the Mark Davises of the world who argue that the expense of eradication is reason enough to give up and let an ecosystem change.

But if and when these techniques are perfected, their use — and the disagreements about them — will be highly decentralized. Right now, when there’s a dispute about whether something causes harm, there’s not a clear framework for how to decide who wins. Peer pressure is a big lever, Moore said. He told me that the Grand Portage tribe and other management agencies responsible for Lake Superior waters have all pushed on each other at various times. If there’s enough peer pressure, he said, it can alter the policies of other agencies, as when the state of Michigan was considering allowing fish farms to operate in the Great Lakes. The Grand Portage Band opposed that decision, he said, and so did a lot of other agencies that manage fish on the lakes. Ultimately, the idea was shot down. Some disputes, though, seem to “persist and persist without really being resolved,” Simberloff said. And Reitz told me that the decisions about which species get tackled and which don’t depend mostly on politics — who can make a case that a problem is big enough to deserve government money.

Even then, a different kind of politics can enter the picture. In the summer of 2016, Florida Keys officials sought, and won, the federal government’s approval to release genetically modified mosquitoes with the goal of eliminating an invasive mosquito population … and with it, the risk of the Zika virus. But local residents didn’t want their island to be a testing ground. The political battle has dragged on in the years since residents voted against the trial — even as a different kind of altered mosquito, this one carrying a bacteria that kills other mosquitoes, were released in another part of the Keys and elsewhere.

The future, experts told me, is likely to be full of scenarios like this, where one group is able to move to eradicate a species, even if other, nearby communities disagree. The shape of the natural world would come down to who has the political power, money, will — and vision.

“It all depends on what we want,” Reitz said. “Is it what people wish and desire [to serve human tastes], or do we want some continuous legacy — some long-term persistence with what nature was in the past? We’re getting to the point with the technology where we need to have these conversations for the first time. Do we want a world of gardens, or something wild and dangerous?”

People gather at the mouth of Minnesota’s Lester River, waiting for schools of rainbow smelt to swim in from Lake Superior. Nobody knows exactly when the fish will arrive, so smelting is a social affair where people share bonfires and beer to pass the time.

For now, the smelt will continue to alter the ecosystem of Lake Superior, and their presence will create something different than what existed in the past. And humans’ reactions will be different too. While many of the folks who gathered to fish on the rocky beach of the Lester River were white men, like the crowds Schreiner remembered from childhood, I did meet one woman, Sam Bo. She was Hmong, a member of an indigenous group from Southeast Asia, many of whom have immigrated to Minnesota.

Bo herself lives in the town of Coon Rapids, a two-and-a-half-hour drive from the Lester River. It was her first time making the excursion, but the smelt, she’d been told, were worth it. Lots of Hmong were smelt fishing now, she said, pointing out several other groups on the beach. The fish are similar to a species native to Southeast Asia, and the Hmong there catch them in much the same way.

Finally, as darkness fell, a man waded chest-deep into the water. Holding a net on a long pole, like a porous frying pan, he swished it back and forth along the bottom of the river and came up with net half full of wriggling, bouncing silver fish. In minutes, all the people on the shore had joined him, waddling into the flow as fast as hip waders and uneven ground would allow. Under the moonlight, with small waves gently nudging both her and the smelt toward shore, Sam Bo pulled up a bounty of fish. And she smiled.

So You Want To Tether Your Goat. Now What?

🚨🚨🚨 “The Riddler” book is out now! It’s chock-full of the best puzzles from this column (and, fret not, their answers) and some that have never been seen before. I hope you enjoy it, and thank you for riddling with us these past three years. 🚨🚨🚨

Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-size and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,4 and you may get a shoutout in next week’s column. If you need a hint or have a favorite puzzle collecting dust in your attic, find me on Twitter.

Riddler Express

From Luke Robinson, a serenading stumper:

My daughter really likes to hear me sing “The Unbirthday Song” from “Alice in Wonderland” to her. She also likes to sing it to other people. Obviously, the odds of my being able to sing it to her on any random day5 are 364 in 365, because I cannot sing it on her birthday. The question is, though, how many random people would she expect to be able to sing it to on any given day before it became more likely than not that she would encounter someone whose birthday it is? In other words, what is the expected length of her singing streak?

Submit your answer

Riddler Classic

From Moritz Hesse, some grazing geometry:

A farmer owns a circular field with radius R. If he ties up his goat to the fence that runs along the edge of the field, how long does the goat’s tether need to be so that the goat can graze on exactly half of the field, by area?

(The great thing about this puzzle, Moritz notes, is that if you get sick of math, you can find the answer through trial and error with your own circular field and your favorite goat, horse, cow, kangaroo, sheep, unicorn, centaur or sphinx.)

Submit your answer

Solution to last week’s Riddler Express

Congratulations to 👏 Stefan Heidekrüger 👏 of Munich, winner of last week’s Riddler Express!

Last week’s Express brought a fill-in-the-blank challenge: What’s the next number in this series?

9, 10, 19, 24, 31, 40, 51, 64, 79, 90, ?

It’s A9.

A9?! What the … ?

The trick to filling in this blank was recognizing that these numbers aren’t in our usual base-10, or decimal, number system. Rather they are in the base-16, or hexadecimal, system. Hexadecimal is often used by computer programmers. And since we only have 10 digits that go with our usual base-10 system, base-16 uses the letters A through F to represent the values 10 through 15.

OK, back to our series. The pattern is \((N+2)^2\), where \(N\) is the number’s position in the sequence. So the first number is \(3^2\), or 9. The second number is \(4^2\), or 16, which is represented as 10 in hexadecimal. The third number is \(5^2\), or 25, which is 19 in hexadecimal. And so on. Our missing number is \(13^2\), or 169 — or A9 in hexadecimal.

Solution to last week’s Riddler Classic

Congratulations to 👏 Eric Roshan-Eisner 👏 of San Francisco, winner of last week’s Riddler Classic!

Last week you were brought in to solve a serious problem at the Riddler Intelligence Agency, or RIA. Namely, the RIA had been infiltrated by spies, and your job was to root them out. There were N agents total, and K of them were spies. You knew the values of N and K but not, at first, the identities of the spies. You could send any number of agents on a remote island retreat as many times as you wanted. If all of the spies were on the retreat, they would assemble for a secret spy meeting; if any of the spies were not on the retreat, the meeting would not take place. The only thing you learned from each retreat was whether or not this meeting happened.

It cost $1,000 per person to send agents on these retreats. What was the least you could spend while still identifying all of the spies? Assume you knew that N = 1,024 agents and K = 17 spies.

This week’s winner, Eric Roshan-Eisner, explained that it will take at least 122 retreats to identify all the spies: The total number of possible spy configurations within those 1,024 people is N choose K, or about \(4\cdot 10^{36}\). That number is very big — but it doesn’t mean we need that many retreats to suss out our spies.

Think of each retreat as a moment to learn one bit of information about the arrangement of spies (that is, whether or not the spy meeting occurred). I’m using “bit” there intentionally — the key to solving this puzzle is to translate that \(4\cdot 10^{36}\) number into binary, a number that needs 122 “bits” — one digit in a binary number — to be expressed. Every retreat you organize returns to you exactly one piece of yes-or-no, 0-or-1 information — that is, whether or not the spy meeting happened. That’s your bit. Therefore, the minimum number of retreats necessary to differentiate between all four undecillion possibilities is 122. The exact strategy you should use to do this, Eric wrote, is left as an exercise to the reader.

Others picked up the baton there. Tim Black, a grad student at the University of Chicago (Go Maroons!), found a strategy to identify the spies in 131 retreats, and also proved that it is impossible to do so in fewer than 122.

Thomas Swayze also found a 131-retreat strategy, which cost about $93 million. Thomas wrote that his strategy to find the spies was to use a form of binary search to single them out one by one: Start with some subset, S, of the agents that we know contains at least one spy. Then pick a subset, T, of S, and keep the agents in T at home while sending the entire rest of the agency on the retreat. If there’s a meeting, we know that T contains no spy — so leave all the agents in T out of all future retreats. If there is no meeting, there is some spy in T. Either way, we now have a smaller set that we know has a spy. Once we’ve outed one spy, we send him on all future retreats and repeat the process to find all the remaining spies, one by one. The tricky part is deciding how big to make the set T. It depends on the number of agents left, the number of spies we’ve caught, and the size of the set S. Thomas was kind enough to share the Python code he used.

Finally, Laurent Lessard described a strategy that used more retreats (191) but cost less (about $66 million).

But hey, if identifying spies were easy — or cheap — everybody would do it.

Want to submit a riddle?

Email me at [email protected]