Исследователи используют сложные логические задачи для изучения когнитивных способностей человека и животных

More than two thousand years ago, Sophocles wrote his famous work, Oedipus Rex. In it, he posed perhaps the most well-known riddle in history: “What goes on four legs in the morning, two in the afternoon, and three in the evening?” The answer? A human—since we crawl in infancy, walk on two legs throughout our youth, and eventually use a cane in old age. Needless to say, the humans that came before and after Sophocles continued making word puzzles of their own. This sort of fascination is one thing that makes humans distinct from many of the other animals roaming the Earth. Some researchers believe that our ability—or inability—to solve certain riddles could shed some insight on the human mind. For instance, in a 2023 study published in the journal Judgement and Decision Making used four “stumpers,” or tricky riddles, to reveal human biases. Likewise, we also use puzzles to qualify the intelligence of ourselves—and other beings. Take a standard IQ test, for instance. (Granted, they aren’t the most accurate measure of intelligence.) The test might prompt you to continue some sort of number sequence or decipher a visual pattern to measure how strong that squishy, pink control center in your cranium really is. As for animals, this might look like an octopus solving a puzzle as evidence of cognition. In short, our obsession with these brainteasers tells us much about ourselves and the world around us. Here at PopMech, we love mind-bending math and puzzles that will test your critical thinking, logic skills, and ultimately your determination. The following riddles are particularly punishing problems—so go grab a pencil and a piece of scratch paper and prepare to rip your hair out (in the best way). And be warned: They get harder as you go on. No cheating! (Think you’ve cracked the case? Click the link at the bottom of the page to check your answers!) King Nupe of the kingdom Catan dotes on his two daughters so much that he decides the kingdom would be better off with more girls than boys, and he makes the following decree: All child-bearing couples must continue to bear children until they have a daughter! But to avoid overpopulation, he makes an additional decree: All child-bearing couples will stop having children once they have a daughter! His subjects immediately begin following his orders. After many years, what’s the expected ratio of girls to boys in Catan? ➡ The Hint The likelihood of each baby born being a girl is, of course, 50 percent. The Tale of Four Knights ➡ The Problem Legends tell of four knights, standing in a line before the royal court. Each knight wears a different colored cloak, wields a different weapon, and uses a different animal as their emblem. The Golden Trout stands left of the Blue and Green knights. Neither the Hawk nor the Lion wields a Spear or a Sword. The Axe and Sword stand side-by-side, as do the Stag and Lion. Red and Green stand at the ends of the line, and the Sword and Stag stand in the middle. The Green knight wields a Mace. Can you figure out the details of each knight from just these clues? ➡ The Hint Try putting four knights in a simple line, listing what qualities they might have, and cross them out when you’ve eliminated them as an option. A Life-or-Death Game ➡ The Problem In a remote prison, three prisoners are serving a life sentence. The guards decide to play a game with the inmates to pass the time. They have a trunk of hats, and they show the prisoners there are five hats in the trunk—three black hats and two white hats. The guards make the prisoners sit in chairs and line them up three in a row, such that the prisoner in the back of the line can see the two in front of him, the prisoner in the middle can see the one person in front of him, and the prisoner in the front can see nothing but the prison wall. The guards blindfold the prisoners, and place a hat on each of their heads. They then remove the blindfolds and tell the inmates that they can go free if they correctly name the color of the hat they have on—but if they guess wrong, they will be shot dead. Needless to say, the prisoners cannot see what color hat they have on their own head. The guards first ask the prisoner in the back of the line, “what color hat do you have on?” He says he doesn’t know. They ask the man in the middle, and he also doesn’t know. When the guards ask the prisoner in the front of the line what color hat he has on, he answers correctly, and goes free. What color hat did the man at the front have on, and how did he know? ➡ The Hint Pretend that you are the prisoner in the back of the line. What do you see? Then pretend you are the prisoner in the middle of the line. Locker Lunacy ➡ The Problem There are 100 lockers that line the main hallway of Chelm High School. Every night, the school principal makes sure all the lockers are closed so that there will be an orderly start to the next day. One day, 100 mischievous students decide that they will play a prank. The students all meet before school starts and line up. The first student then walks down the hallway, and opens every locker. The next student follows by closing every other locker (starting at the second locker). Student 3 then goes to every third locker (starting with the third) and opens it if it’s closed, and closes it if it’s open. Student 4 follows by opening every fourth locker if it’s closed and closing it if it’s open. This goes on and on until Student 100 finally goes to the hundredth locker. When the principal arrives later in the morning, which lockers does she find open? ➡ The Hint Make sure you pay attention to all of the factors. Tracking Down a Trickster Turkey ➡ The Problem A week before Thanksgiving, a sly turkey is hiding from a family that wants to cook it for the holiday dinner. There are five boxes in a row, and the turkey hides in one of these boxes. Each night, the turkey moves one box to the left or right, hiding in an adjacent box the next day. Each morning, the family can look in one box to try to find the turkey. How can the family guarantee they will find the turkey before Thanksgiving dinner? ➡ The Hint If you simply search one box per day, starting with 1 and finishing with 5, you might not find the turkey. It could be in box 3 when you check box 2, and then move to 2 the next day when you check 3, and you would miss it. Similarly, you cannot keep checking the same box, as the turkey could bounce back and forth between only two boxes the entire time. You need a plan to guarantee you will find the turkey. The Solutions Think you’ve solved these tricky riddles? Check your work—or learn how to solve the brainteasers—here. Editor’s note: Jay Bennet, Laura Feiveson, Emma Frederickson, and Richard Malena contributed to this story. ➡ Every Single Drone Fighting in the Skies Over Ukraine ➡How to Buy a New Car in 2022 Without Getting Fleeced ➡ This Megastructure Could Keep Us Alive Forever