by Fred Stang
“You see, one of these machines is making a slightly heavy wedge of cheese. One ounce too heavy, to be precise. One tenth of our cheese wedges weigh one pound and one ounce instead of the required pound they are supposed to weigh. You can have a couple of the heavy ones, but first we need to know which machine is making the heavy wedge.”
“And you can’t tell just by looking, I suppose,” Tollie said, already knowing the answer.
“No, they all look the same. But we do have a scale.”
“Then we can just weigh the wedges coming from each machine, taking ten weighings at most, and find out which machine is making heavy wedges, can’t we?” Tollie asked, still harboring a feeling that this would be too simple to be a possible answer – for, then, what would be the problem?
Young Chef pointed to a truly huge scale in the corner. “It has a large pan you can put the cheese wedges on and it has a digital readout, giving the weight in pounds and ounces. Our problem is that it will shut off after one more weighing, and then we will never be able to turn it on again. Some malicious hacker got into its inner computer and put in a swatch of computer code that causes it do shut down forever after a certain number of weighings. We cannot fix this, we will have to send the machine back to the manufacturer. But we would like to find out which cheese machine is making the heavy wedges of cheese before we send the scale away. We are hoping to do this using up the one weighing we have remaining.”
“Could it not be that this same malicious hacker also caused one of the cheese machines to put out heavy wedges of cheese, just to mess up your output?” Tollie asked.
“It is possible,” Young Chef admitted. “Frodlaw Cheese is famous the world over for its tart flavor and consistent quality. It used to be made only for the hotel, but the demand for it grew so great that we enlarged the factory to accommodate the cheese lovers. We need to maintain our reputation for consistency and our wedges need to all be one pound, so we can package them uniformly and ship them out. So, the sooner we can identify the problem machine, the better. I just hope there is a way to do it with just the one weighing.”
“That’s a tough one!” Tollie exclaimed. It seemed on the surface of it to be the hardest challenge yet posed to them.
Mouse was all ears, even as his nose still quivered at the delectable cheese aroma he could not resist. Tollie needed a hint, and that was his job. He held his paws together in front of him, mentally composing a good hint. It should not give away the answer, but it should help Tollie come to one. “That scale,” Mouse said, indicating it with a broad sweep of his right paw, “gives you a reading in pounds and ounces. If you took one wedge from the first machine, it would give you a reading of one pound, or one pound and one ounce, depending on whether or not the first machine is the defective one. You can put any number of cheese wedges on the scale. You can see it is large enough to hold many of them.”
Mouse stopped. This was it, the whole of his hint. Tollie’s face must have shown his disappointment, because Mouse added apologetically, “It’s a good hint if you can follow it forward.”
Tollie accepted this, as Mouse had never led him astray. So he thought on it.
And thought on it over and over, though no solution seemed to be presenting itself. Young Chef and Mouse were looking everywhere except at Tollie, politely giving him time for his reflections.
“One pound and one ounce,” Tollie thought out loud. Then he fell silent again, still not getting past this to any broader solution that would take into account all of the machines. “If the first machine is not the heavy machine the scale would read one pound and zero ounces. If it was the heavy machine, the scale would read one pound and one ounce…”
After a long while, Mouse relented. “Ten machines. You can take all the wedges you want from each of the machines…” He let the suggestion linger in the ensuing silence.
Tollie had heard him, of course, but he was still not seeing how it would help him in any way. “Any number of wedges from any of the machines, or even all of the machines… Pile them up on the scale… Read the total weight in pounds and ounces… Then identify the heavy machine…”
It came to him in a flash, like so many of these new challenges. He had read about that somewhere, he remembered. It was called the “Aha!” reaction.
He composed himself at once, for he had the solution now in his mind.
“Take one wedge from the first machine, two from the second, three from the third, and so on until you have taken ten wedges from the tenth machine. Put all of these on the scale and take your one reading.”
Young Chef looked at him quizzically. Mouse was starting to get excited. Tollie, he knew, had the answer, and soon he, Mouse, would have cheese! It was like being in Heaven.
Tollie explained. “Your reading will be in pounds and ounces. If you took one wedge from the first machine and two from the second, and one of those two machines was the heavy machine, you would get a reading of either three pounds one ounce, if the first machine was the heavy one, or three pounds two ounces, if the second machine was the heavy one. This would be because you had one wedge from the first and two wedges from the second machine. You can follow this through to all ten machines and use the same logic – extrapolation. Say, you had on the scale ten wedges from the tenth machine and it was the heavy machine. The reading would be a number of whole pounds and ten ounces more. The number of ounces over the even pound weight will tell you the number of the heavy machine.”
Young Chef slowly came around. “Yes, it would…”
Mouse coughed discreetly.
“Oh, yes, it would, of course. And I must thank you. And, I do owe you each a wedge of the cheese, and I will make sure it is one of the heavy ones, just as soon as I carry out the weighing.”
Mouse looked a bit put off. He would have been happy to just have a wedge of cheese right now, but he saw that Young Chef wanted to be generous, and he would, after all, end up with an extra ounce of cheese!
While Young Chef was performing his weighing, Tollie noted to Mouse, “We have been here a long time. It seems like we were just led along from one thing to the next ever since we met Young Chef.”
“Oh, of course,” Mouse said, “this is what is called ‘surfing the net.’ Sometimes you just find yourself being carried along by the links that hold this world together, and you can find many new things that you would not have thought of if you did not pursue your natural curiosity.”
Tollie considered and felt he had, indeed, enjoyed the random encounters as they had provided him that pleasure that can derive from the unexpected.
“But,” Mouse continued, a bit of warning in his tone, “you will have to be careful where this curiosity takes you or you can end up in a dangerous place. There are all kinds of things here and all kinds of people and creatures. They are not all safe. Just be careful. So far it has been all right, because Young Chef is an honorable man.”
“He is that,” Tollie agreed. “And I can see that there would be dangers in this world, just as in that ‘real’ world I come from. You are a creature of this world, so you understand it better, but it is understandable anyway, because of the similarity between the worlds.”
Mouse smiled enigmatically, wishing it were this simple. But he had faith that Tollie had natural common sense in addition to his natural curiosity.
Tollie felt it was time to go and placed his hand on Mouse’s back. A helicopter appeared and landed next to them.
“You are figuring out one thing, aren’t you, Tollie?” Mouse suggested.
“What’s that?” Tollie asked.
“Oh, the little matter of who is in charge here,” Mouse said, an enigmatic smile playing across his face. “You are, of course.”
“Let’s get aboard,” Tollie said eagerly, because he had always wanted to ride in a helicopter and here was his chance. It was a virtual helicopter, of course, but it was still exciting. For the moment he did not realize that he was indeed in charge, but Mouse realized it and was happy f
or Tollie. He went along and clambered aboard the helicopter, his chunk of cheese in hand. Whoever was in charge, Mouse had his cheese!
CHAPTER 11
THE FRIENDLY ISLE OF AMITI
The pilot welcomed them aboard. “I’m Madison, but you can call me Maddie,” she introduced herself. “It’s good to have you, just take your seats and fasten your seatbelts. We are going over the ocean, just as Tollie wanted.”
Mouse just nibbled at his cheese, while Tollie wondered at the seeming miracle that Maddie knew just what he wanted.
They were off!
In the distance lay a small, long island, and as they got closer, they could see that there was a commotion there, trouble.
“That is the island of Amiti,” Maddie told them. “It is known for the friendliness of its people, the Amitians, a people small in size, but large in generosity and kindness. They are also called the Friendly Islanders. They always welcome strangers with arms outstretched and go out of their way to accommodate the needs of their visitors. So, if they are in trouble, we should help them.”
“Let’s get closer and take a look,” Tollie said.
Mouse put aside his hunk of cheese for the moment, to pay attention to what was transpiring on the Friendly Isle of Amiti.
As they got closer, they could see just what the trouble was. The islanders were gathered together at one end of the island, while a large fire moved toward them from the other end of the island, having already burned down their village. The islanders had left only the possessions they had been able to carry.
Their king, Iti Biti Amiti the Fifty-Fourth, stood tall (at 5’ 2 ½”) among his people, seeking counsel and a way out of their dilemma. The island was ten miles long and the fire was approaching them, at a speed of about five miles an hour as it happened, as the prevailing winds were this speed and heading in their direction. King Iti Biti Amiti was trying to figure out a way to save his people from being consumed in flames as the fire inexorably approached. They did not have much time.
Tollie took this all in as they approached. “We must land next to them,” he told Maddie. She took the helicopter down and they disembarked to join the Amitians and their king.
Even though they were in dire straits, the Amitians welcomed them with their customary warmth. “Welcome to Amiti,” King Iti Biti greeted them. “We would love to invite you to share a meal with us, but, as you can see, we are having a problem here. Maybe you can help us?”
“Of course, anything we can do, we will do,” Tollie answered, and Mouse and Maddie nodded in agreement. “We could just take off in our helicopter, but we could not take your people with us, so we must come up with a solution and that fire is approaching quickly!”
“I know you cannot take us with you, but what can we do? Whatever it is, we must come up with a plan fast.”
Tollie thought on this. Mouse looked on and did not seem to have a clue for him this time. Maddie was concentrating, looking at the raging fire despairingly. How could the Amitians be saved?
“The fire is coming on strongly,” Tollie said. “We must somehow stop it and stop it before it reaches the people of Amiti. It is about six miles away now, a little more than an hour away, and the edge of your island, the far coast, is about two miles in the other direction. You cannot just run from it. That would at most buy you a little time, but it would not save you. You would run out of space to run.”
“That is correct,” the now even more forlorn Iti Biti Amiti acknowledged. “At this point I just want to save our people.” The islanders all looked morose as their King did not seem to know what to do and none of them were seeing a way out either. “If we can survive this fire, we should be all right. Dry season will soon be over and we can rebuild the village and re-grow our food supply, and there are plenty of fish we can eat in the meantime.”
Which prompted a thought in Tollie’s mind. “Why can’t you just go in the water?” Tollie ventured, giving what seemed an obvious solution.
“Ah, would that we could,” Iti Biti replied. “But it is unsafe. At this end of the island the ocean is full of sea beasts that would simply destroy us in the water. We can swim and fish at the other end of the island. That is why we built our village there. For some reason the sea beasts do not go there, so it is safe for us to swim near the village.
“Or, where the village was…” he corrected himself. “But the fire prevents us from getting into the waters there. It is too late.”
Tollie wanted to ask about these sea beasts, but realized this was not the time for his curiosity to reign, but, rather, time for him to rein it in! They were probably sharks, giant squid, or octopi and such, he reasoned. It did not matter, anyway, for if the Amitians believed in these “beasts” they were as real as anything else to them, and nothing could get them to enter the waters here.
Tollie glanced into the distance, rapidly closing, at the coming fire. It seemed nothing could stop it as it consumed everything in its path. The thought of the fire “consuming” everything stuck in his mind, and he ran it over and over in his considerations.
Of course! A fire could not burn if it had nothing to consume. It had to have fuel. Remove the fuel and the fire would die.
“I have an idea,” he addressed King Iti Biti Amiti.
Iti Biti regarded him gravely. “Whatever it is, we need some answer and a realistic course of action.”
“We must set fire to the island from here to the far coast, which is about two miles away. We set the fire and then follow it to the edge of the island and wait there. When the big fire reaches the land that has already been burned, it will go out, since it will have nothing to burn for fuel. The land and everything on it that is flammable will have already been used up by our little fire.”
Iti Biti nodded. “Yes, that would work. The entire island would still be burned up, but all of us would survive.”
He turned to his people, drawing himself up to his full height, and explained to them what must be done. They listened, doubtful at first, but then understanding that setting another fire would, oddly enough, save them from the approaching fire they now faced. They set about gathering kindling to give their new fire a good start.
Iti Biti watched them, hope showing in his expression for the first time. “I must thank you, Tollie. You certainly came up with what seems the only solution to our problem.”
Mouse chimed in. “Tollie has become quite good at solving different problems. It is his challenge here in our world-wide web and he has been rising to the occasion each time he has encountered a new challenge. He has learned much since I first met him.”
“A good thing for us,” Iti Biti said, watching as his people set the smaller fire that was to burn the land between them and the coast.
The new fire took, and burned in the direction of the wind, burning the two miles between them and the other end of the island as the original fire approached from their other side. The two miles burned up after some minutes and the islanders began to run over the burned land, away from the big fire. They would be safe now, since the big fire would stop here, having reached the scorched land and having nothing to fuel it.
“I must take my leave of you and go with my people now,” Iti Biti said. “Thank you for your help! But, you must now go, too. Come back in a year and we will have a wonderful feast for you and your friends!”
“Thank you, we surely will,” Tollie said. “Good luck!”
King Iti Biti joined his people heading away from the fire and escaping to the safety of the island’s end. Tollie, Mouse and Maddie climbed into the helicopter and lifted off. Amiti grew small in the increasing distance as they flew away, but they saw the big fire reach the burned land and expire in a matter of minutes, no longer a danger to the Amitians, who, huddled at the end of the island, watched gratefully as the last flickers of flame died away.
They waved at the Amitians from their distance and saw them wave back before the helicopter traveled too far away to see the island any more.
&nb
sp; “A nice people,” Tollie observed. “I hope they will be all right.”
“They will be fine, Tollie,” Maddie told him. They will fish for food until the wet season comes and then they will rebuild. Their lives are simple but comfortable and they will rebuild their village happily. It will take some time. After all, the plant life must return and grow enough for them to get material.”
Mouse pulled out his cheese now and nibbled at the remaining hunk, which, Tollie noticed, was much smaller now than the original. Mouse had been nibbling while he had not noticed.
Seeing him eye the cheese, Mouse explained, “I was nervous for the Amitians and when I am nervous, I nibble cheese. It comforts me.”
“Where to?” Maddie asked. Mouse looked at Tollie expectantly.
CHAPTER 12
THE TRUTH OF THE MATTER
Tollie took a bite of his own cheese and some apple to chase it down. “Let’s go to another island. I like islands.”
“Island it will be then,” Maddie announced. “See that one in the distance?”
Tollie and Mouse squinted. They saw an island about the size of Amiti, but holding two villages. It was more lush than Amiti at this time of year and had much plant and tree growth and more mountainous region. They could see the two villages clearly now. They were of roughly equal size and well-built, with stone cottages and cobblestone-paved streets. Small villages but well laid out, with clear main thoroughfares and a number of offshoot streets dotted with cozy houses.
“This is the True-False Island,” Maddie told them. “It is so called because it has two villages on it and the inhabitants of those villages are quite opposite to each other. In one village, only the truth is told, while in the other only lies are told. Otherwise, you cannot tell the villagers apart, different as they may be in their capacities for truth-telling. I will take you down and you can see for yourselves.”
She landed the helicopter delicately, finding an open flat area where they could step off easily. When the rotors calmed, the three disembarked. “You explore,” Maddie said. “I will have to stay with the helicopter.”