Banana Fever: Short Division

[Music] Once upon a time in one of the great tropical forests that sprawled across the equator, there lived a monkey called Max. Max had a passion for bananas, and every morning with great gusto and delight, he would eat all the ripe, juicy bananas he had picked the night before. And afterward, totally content, Max would scamper off to play with his [Music] friends. One morning, Max found his friends in a state of great excitement. The vine was moving by itself. I've never seen anything like it. And a bunch of bananas picked themselves and floated off. Can you imagine that? I can vouch for them both. I saw it, too. I couldn't believe my eyes. Hey, you guys must have been dreaming. [Music] And the same day, he found a bunch of bananas so ripe and lovely that he never gave the slightest thought to what his friends had told him that morning. The next morning, Max woke up earlier than usual and slipped down the tree to his bunch of bananas. But instead of a bunch, the bananas were spread out in a line, and some of them were gone. I don't understand it. This has never happened before. I'll bet my pals think they're pretty clever. They must have taken those bananas. Somehow, breakfast just wasn't the same. And Max was so annoyed by his friend's cruel joke that he decided to go and straighten things out. But his friends denied taking any of the bananas, which made Max even angrier, and he went off muttering and spluttering. That evening, his anger cooled somewhat when he found 15 almost perfect bananas. 15 bananas. 15 lovely B. But the next morning it had happened again. This time the bananas were spread out in two rows of five or 10 bananas in all. Max had 15 bananas, and someone had taken five of them. The mere thought of this made him purple with rage, and when he found his friends, he was too angry to speak. With great effort, they convinced Max that none of them had taken his bananas. That night, as Max headed for home with a new bunch of 12 bananas, we saw it again. Saw what? the swinging vine with no one on it. It was very scary. Max wasn't entirely convinced, but he nonetheless decided to stay awake and guard over his bananas. He waited and waited, and then when night was at its darkest, the bananas started to move by themselves. They moved into three rows of four bananas each. And then they moved again into two rows of six bananas each. Max stood a gas as one row of six bananas rose up into the air and floated away. Stop. Come back with my bananas. The next morning, a humble Max told his friends what had happened. Whatever it is, it's invisible, but it must be stopped nonetheless. I'll stand guard with you tonight, Max. We'll try to catch the thief. That afternoon, they picked nine delicious bananas. That night, after having placed the bananas on the ground near his tree, Max pretended to sleep, and the giraffe did her best to hide in some bushes nearby. Shortly after midnight, the bananas began to move. They moved into three rows of three bananas each. Then one whole row rose up and floated away. [Music] Rabbit. This time, let's use a trap. So Max and his friends spent the day digging a deep hole and covering it with large leaves. Then Max carefully placed nine bananas on the leaves, for by this time his passion for bananas had turned into grim determination to catch the banana thief. That night, Max and the giraffe waited once more, but they were so tired from building the trap that they soon dozed off. Whatever it was, the invisible thief was trapped. So Max told the giraffe to stick his head into the hole and feel around. Help. It's got me. Hey, it's crawling up my neck. The invisible thief had gotten away with three of Max's nine bananas again. The following day, the alligator called them all together. I have a feeling that we're not going to capture this invisible thief, but we can prevent him from stealing as many bananas as he has been. But how? Most thieves do things in a certain way. Let's review the thefts and see if there's a pattern to them. Let's see. The night I brought home 15 bananas, he took five of them. And then the next time I brought home 12 bananas, he took six of them. And both times that I had nine bananas, he took three of them. H what? Well, five divides 15 evenly, 6 divides 12 evenly, and three divides 9 evenly. What do you mean divides evenly? The alligator explained that if you have 15 bananas, you can split them into groups of five and you'll have none left over. And if you have 12 bananas, you can split them into groups of six and have none left over. and continue the alligator. If you have nine bananas, you can split them into groups of three and have none left over. I think I figured out his pattern. When I had 12 bananas, he first put them into groups of four, but then change them into groups of six. Four divides 12 evenly and six also divides 12 evenly. So he took six which is the larger divisor. That's his pattern. He always takes the larger divisor. Well, how come he didn't take all 12 bananas? 12 is the largest divisor of 12. Because he never takes all the bananas. That's part of his pattern. Isn't there a number of bananas I could gather where he'd take nothing? I'm not sure. Well, if he takes only three bananas when I have nine, what about 10? But they found that five divides 10 evenly. So 10 wasn't a good number since a thief would take five. Then they tried 11 bananas. 11 could not be divided into groups of two evenly. And it can't be divided into groups of three evenly, nor groups of four, nor five, nor six, nor seven, nor eight, nor nine, nor 10. Only 11 worked. So Max went out and collected 11 bananas. And that night he waited and watched and sure enough the bananas began to move. First they moved into a shape like this and then a shape like this and finally they moved into a shape like this. Max held his breath. He was sure the thief was going to take them all. But just as the alligator had predicted, the thief didn't take all the bananas. and one is the only other divisor that can be divided into 11 with no remainder. He had stuck to his pattern. Oh well, I guess I can afford to lose one banana from the bunch. Several weeks later, Max's cousin Alvin came to visit. After a delicious dinner, Alvin laid back and groaned with satisfaction. That's the first full meal I've had in weeks. And why is that? Because someone has been taking most of my coconuts. I guess one banana wasn't enough for him. For who? Have another banana and I'll tell you all about it. [Music] What happened?