by Fred Stang
“He has 467 miles to go to the oasis and his fellow hungry camels. This means he will eat 467 of the 1,001 bananas, leaving him 534 bananas when he finally arrives!”
Tollie let out his breath. He had concentrated deeply to get this result.
“Mr Camel, I think 534 is the most bananas you can get across to them. I hope that will be enough?”
Camel thought this over. “Yes, yes,” he said at last. “I believe you have it right, and, yes, 534 bananas will be enough. My friends will only have to travel 100 miles to the coast, where they can get the food they need. There will be five of us, including myself, naturally. So, there should be more than enough! We could even eat a few before we set out. I don’t know how to thank you.”
“A camel in need is a camel indeed,” Tollie said graciously.
“Well, I better get going,” Camel announced a little apologetically. “They are waiting for me.” He trotted off, a swagger in his walk. He knew he would be a hero among his fellow camels when he got to the oasis.
Mouse and Tollie watched him go. He would at least be traveling in the evening, so it would be cooler for him. Tollie felt good. He had been able to help. Mouse said, “A good deed nicely done. You are learning and growing here, Tollie.”
“I think you’re right, Mr Mouse. I really was glad to help Ancient Egyptian and Camel. I like that I could find the answers they needed. I think I learned that from Carl. He was quite a kid, wasn’t he?”
“Oh, yes, I would say so,” Mouse said, with a wry smile.
For the first time since he had entered this brave new virtual world, the full sense of its wonders and possibilities hit Tollie. It seemed he could just think of anything and Mouse could get him there. So many choices, so many things to do, so many places to go. Where to now? He was not feeling the least bit tired, though it felt to him that they had done a lot of traveling together so far. Time, too, passed differently here. The little clock in the corner showed only about half an hour had passed, though it seemed quite a bit longer to Tollie, in spite of not feeling tired as he surely would in the “real” world. This was a very different place.
Unconsciously, he rested his hand on Mouse’s back. He was becoming used to this, comfortable with it, it seemed the only natural thing to do. His reflections on time, however, led Mouse to transport him to a kitchen, of all places. Well, where else would one use a timer?
CHAPTER 7
TWO TIMERS – THE HARD-BOILED EGG STORY
An obviously inexperienced young chef, no doubt an apprentice, was looking very worried. The reason soon became clear as he gestured toward two egg timers on the counter, the kind that measures a specific amount of time by allowing a certain amount of sand to pass through the narrow middle neck of an hourglass container.
The egg timers were clearly labeled “7 minutes” and “11 minutes.”
“But,” Young Chef groaned, “I have to hard-boil an egg properly, which means boiling it for exactly 15 minutes, to get it just right. There is no 15-minute timer!”
“Let’s think about this methodically,” Tollie said with a newly found confidence. “There might be a way to do it with the timers you have.”
Mouse remained silent, but Tollie knew his body language well enough by now to know that Mouse knew there was indeed a way.
“Please,” Young Chef implored him, “if you can help me I would be ever so grateful.’
Mouse took a seat and listened. It was a tough puzzle but this time he offered no hint. He hadn’t been asked for one. He thought Tollie could solve this one without any hints.
“Something to do with the difference between 7 minutes and 11 minutes.” Tollie did his thinking out loud. “”Not the simple addition because 7 plus eleven is 18, too many minutes. But, then, 11 minus 7 is 4, too few minutes. Of course, 4 plus 11 is 15, the right number of minutes to hard-boil the egg perfectly.”
Young Chef listened to him eagerly. “Yes, somehow we must get 11 and then 4 minutes. We have the 11 simply enough from the timer, but how to get the 4 additional minutes?”
Tollie thought in silence for a while. Young Chef waited. Mouse sat relaxing, not looking worried at all, at all. This did not irritate Tollie this time, since he believed Mouse was relaxed because he thought Tollie would solve this challenge, as well as he had now solved two in a row. Mouse believed Tollie was a good learner. Carl Friedrich had hinted at something of the sort as well. So, he applied their advice now. The starting point was to believe there was an answer.
“Let’s try turning them both over, starting them both off at the same time.” Tollie paused, his face scrunching up just a little. Then he resolved something in his mind and continued.
“When the 7-minute timer runs out, turn it over again!” Here was the key he had figured out. “Now, when the 11-minute timer runs out, the egg has cooked for 11 minutes total. We need 4 more minutes. There are 4 minutes on the bottom of the 7-minute timer. So, turn it over yet again, putting that 4 minutes on the top. When that runs down, the egg will have cooked for 15 minutes and it will be a perfect hard-boiled egg.”
Young Chef was overjoyed. “That will work! Thank you, thank you. Come, come,” he said. “You two deserve a few moments of rest. I can see you would like to sit and stretch your legs for a while.”
He led them through the swinging doors and down a long corridor, emerging in the lobby of the hotel to which belonged Young Chef’s kitchen. The concierge at the desk greeted them cordially. “Of course, you are welcome at the Hotel Frodlaw. Have a seat for a while. Those two easy chairs by the window should serve you well for some relaxation.”
Tollie noted the sign “Hotel Frodlaw” and thought it an odd name for a hotel. But it did seem oddly familiar…
Young Chef took his leave. “I have to cook the egg,” he told them, “but I will return. Enjoy your rest.”
As they rested, they watched as a bustling trio entered the lobby from the other end. Their friends the merry triplets had arrived, hipping and hopping along! Tollie chuckled and Mouse allowed himself a small smile.
CHAPTER 8
THE CASE OF THE MISSING DOLLAR
Hop Hop, Hip Hip and Hip Hop made their way to the desk. Hip Hop beseeched the concierge, “Sir, we have very little money. Can we share a room for the night to defray the cost?”
“Yes, that will be quite all right,” the concierge said. “It will be $30. Will that be all right?”
With much ado about it, the triplets went through their pockets, pulling out even their change to assemble the right amount. Their pleasure was great when they finally got $30 together and gave it to the concierge, who put it in the register and signaled the bellboy over to help the triplets with their luggage.
“Oh, no,” Hop Hop protested, “we have no money left for a tip.”
“It will be my pleasure,” the bellboy assured them. “We all fall upon hard times now and again and you are nice enough men that your good will is quite enough.” And he took their bags and led them up the stairs to their room.
“Nice hotel, this,” Tollie observed.
“Yes, the Frodlaw has always had a good reputation for its service, even though sometimes they get things backwards.”
Mouse stretched and yawned, a quite curious sight, as Tollie had never seen a Mouse yawn. Mouse even covered up the yawn with the plaid sleeve of his jacket.
When the bellboy returned, the concierge summoned him and handed him $5. “I have just overcharged those men for their room. It should have been $25. Please take them the $5 back.” He handed over five single dollar bills, and the bellboy left to return it to its proper owners.
After a while, Hop Hop, Hip Hip and Hip Hop came downstairs, deep in conversation, evidently confused about something. Hip Hip was saying, “We got back $5 and then we tipped the bellboy $2. So, we got back $3 overall, meaning we each paid $9 instead of $10 for the room. For three of us, that means 3 times 9, which equals 27. Then we gave $2 to the bellboy for his tip. That makes $29. What happened to the e
xtra dollar?”
“It is true!” Hop Hop agreed. “We each paid $9 and 3 times 9 is 27, and you add the $2 we gave to the bellboy and get $29. There is a missing dollar! How can that be? What happened to it?”
They then noticed Tollie and Mouse for the first time and hipped and hopped over to greet them, grinning merrily, and, of course, presenting the problem of what they had paid for the room and why there was a missing dollar.
Tollie was perplexed, and even Mouse looked uncertain. The logic was there and the multiplication and addition seemed correct. This was not easy, for, however he looked at it, Tollie could not “find” the missing dollar or explain how it added up to only 29 when it should have added up to 30.
The concierge, having overheard the conversation, came over to help. “This has happened at the Frodlaw before,” he said. “It took us a while but we were able to see the source of the confusion. It is in how Mr Hip and Mr Hop were stating the transactions.”
Tollie, Mouse and Hop Hop, Hip Hip and Hip Hop were all paying close attention. They truly wanted this explained to them, as the missing dollar was bothersome.
“It is true that each of the triplets paid $9, making their expenditure a total of $27. They also paid $2 to the bellboy, but they made the mistake of adding that to the $27, when they should be subtracting it from $27. They were supposed to have paid $25. Add to that the $2 tip for the bellboy and you arrive at the $27 they actually paid. Put another way, they paid a total of $27. Subtract from that $27 the $2 tip and you arrive at $25, the cost of the room itself. There is no addition of $2 to $27. The $2 needed to be subtracted from the $27!”
“I can see it now,” Mouse said. “It is a matter of how they were saying it that led to the confusion.”
“Yes,” agreed Tollie. “It was a confusing of doing addition when it was subtraction that was called for.”
Hip Hip, Hop Hop and Hip Hop giggled, embarrassed at their having made a mess of their calculations.
“It is not a problem,” the concierge assured them. “Several of our guests have done the same. Of course, the first time it happened it was difficult to figure it all out. And, I understand it is my mistake in the first place, for having overcharged you”
“Oh, that is quite all right,” Hip Hop assured him in return. “You were honest enough to return the money, and we got to tip the bellboy after all, so all is well.”
“I am glad to have been of service in clearing up the mystery of the missing dollar,” the concierge told them with a bow, and returned to the hotel desk.
“Well, we must repair to our room and unpack,” the triplets told Tollie and Mouse, speaking in unison as they tended to do, unless, of course, they were confused about something that they needed to discuss among themselves. “Perhaps we shall see you later. In fact, I am sure we will!”
Tollie waved at them, smiling, and Mouse made a convincing “wave” with his “hand.” The triplets jaunted up the stairs, bringing much mirth to all who witnessed them. The ways they moved were funny to behold.
When they were gone only moments, Young Chef returned. “I have a few things to show you. Come with me. You are going to enjoy this. I hope you like apples. And oranges.”
Tollie and Mouse indeed hoped there was food involved. They were hungry and followed willingly. Tollie liked apples. So did Mouse, but he had never eaten an orange, so he could not compare apples with oranges the way Tollie could. Of course, Tollie would eat oranges sometimes, because they were good for you, but they were not as tasty to him as apples. Mouse would have to learn.
CHAPTER 9
APPLES AND ORANGES
Through the swinging doors again and down the long corridor in the other direction now, Young Chef took a right turn and opened the first door, beckoning them with a flourish to enter.
In the center of the room were three boxes, all with labels: APPLES, ORANGES, and APPLES AND ORANGES.
“At least we know where the apples are,” Tollie observed.
“Not quite,” Young Chef said. “You see, all of the boxes have been given the wrong label. You can have all the apples you want, or oranges if you wish, but you must first find the right labels for all of the boxes.”
“That’s crazy,” Tollie objected. “Who would deliberately put wrong labels on them?”
Young Chef shrugged. “It’s a crazy world, what can I say? It might be someone’s idea of a joke. Or, perhaps it was not done deliberately.”
“Indeed,” Mouse said enigmatically. Tollie scrunched up his face. “Crazy indeed,” he said, rolling his eyes heavenward.
“You have to follow the rules,” Young Chef warned them sternly. “You can take fruit out of the boxes, but you must take the minimum number of fruit and you must take them from the minimum number of boxes. Proceeding this way, you must correctly label the boxes with the minimum number of removals from the boxes. Only if you label the boxes correctly can you have your snack of them.”
“Humph!” Tollie snorted. “Silly, but let me work on it.
His face relaxed as he pondered. The minimum number of fruit from the minimum number of boxes. He would have to reason his way to the answer. He believed now that there was an answer!
“If you took one fruit out of APPLES, one out of ORANGES, and all of the fruit out of APPLES AND ORANGES, you would know the answer and could label the boxes correctly. But that seems excessive. The problem calls for a simpler answer, only because it has been presented as a problem, and you would not do that if there were not a simpler answer than just using ‘brute force’ to get them labeled right.
“So, let us look at the unique case. The box labeled APPLES AND ORANGES is the only one with a dual label. The other boxes name only one fruit. Let’s pull a fruit out of APPLES AND ORANGES.”
Tollie reached in and pulled out an orange.
“Now, this box must contain oranges, as I have here an orange and the box cannot contain apples and oranges, for it is mislabeled. It has an orange in it and so it cannot be APPLES. Again, it cannot be APPLES AND ORANGES because that label is wrong. Let us therefore label it ORANGES now, and we have labeled one of the boxes correctly.”
Young Chef and Mouse nodded in agreement.
Tollie continued, “The box that is labeled APPLES cannot contain apples because the label is wrong. And it cannot contain only oranges because we now know where the oranges are. So it must be labeled APPLES AND ORANGES, the only option remaining. And, that leaves the box labeled ORANGES, which must contain apples only as that is the only label left, and we must label it APPLES.
“If you had pulled out an apple instead, you would just reverse the procedure.”
“Let’s see,” Young Chef said, switching the labels according to Tollie’s answer and then opening the boxes to find them correctly labeled as Tollie had indicated. “Apple, anyone?” he asked.
Tollie took an apple and thanked Young Chef, who then offered one to Mouse. “Here, Mr Mouse, have one yourself.”
Mouse took the apple and slipped it into a large pocket in his ridiculous plaid jacket. Tollie failed to completely stifle a laugh. Mouse looked a bit offended but it quickly passed. “I am saving it for later, when I hope I will have some cheese to eat with it. For now, I would like to try an orange. There is always the opportunity to be considered to try something new.”
“Cheese, eh?” Young Chef mused. “There is a possibility that we could get some cheese for you, but, here, have yourself an orange for now.”
Mouse looked at the orange dubiously. He could not see just biting into it like you would an apple.
“Here,” Young Chef offered, “let me peel that for you.”
He did so and handed mouse a wedge of orange. Mouse nibbled at it and drew in his cheeks. “That is potent,” he said. But he ate it and another, and shared the rest with Young Chef and Tollie. Tollie was hungry enough by now that he had eaten the apple and was glad for some of the orange as well.
“You mentioned a possibility of cheese, Young Chef?” Mouse
asked eagerly.
“Oh, yes,” Young Chef responded quickly, “I am having a little problem with our cheese machines and if you can help, you can both have some cheese. Tollie, save an apple for yourself, you can have it with cheese. Mr Mouse, I know you have your apple ready for cheese.”
“Cheese!!” Mouse said with relish. He loved cheese, as mice will.
CHAPTER 10
THE BIG CHEESE
Young Chef led Tollie and Mouse back to the long hallway, and took them to the furthest door, at the end, facing them. He solemnly opened it with an impressive flourish. They entered a fully working cheese factory, which to Mouse was about the most wonderful thing in the world.
The pungent odor of cheese set Mouse aquiver. His eyes gleamed with excitement and he wriggled his nose animatedly, his entire being suffused with sheer anticipation. He could barely contain himself.
Ten machines along one wall clanged, whirred and made strange hissing and slicing noises, spitting out wedges of cheese onto a conveyor belt. Tollie thought one of them would last him a whole day, so large were the wedges. Mouse looked on, struggling to maintain his customary patient composure. “How much does one of those wedges weigh?” he asked, trying almost successfully to maintain a calm exterior.
Young Chef said, “Funny you should ask. They are supposed to weigh one pound each.”
“Big hunk of cheese,” Mouse observed. “But I certainly would like one!”
“You can both have one but you must first help me with a little problem we are having.”
Tollie sighed. Ever since entering the World-Wide Web, this blooming buzzing virtual reality, he had been faced with one problem after another. By now he could tell when yet one more was coming up. But Mouse waited eagerly to get on with it. Even if they had to earn their cheese, he wanted to move things along.