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Sunday, January 10, 2010

8th Grade Problem of the Week: Chapter 9: Harvesting

       Teena and Oto, the leaders of a very young tribe of tree dwellers, proved to be excellent hosts. They had saved Jake from some life threatening attack (which he still did not understand) and provided food and shelter for his Aunt and the other shipwrecked passengers once they had calmed down and understood that Jake had not been kidnapped in reality. Justin was instrumental in convincing the Captain, as well has his mother, that they were not in any danger. It wasn’t that he knew this for a fact. It was more of an intuitive feeling. Something in the serene and joyful voice of Teena inspired confidence. He felt safe.
For her part, Teena seemed to be drawn to Justin and Jake as well. She showed them around the village, which was built inside a grove of huge mango trees. The villagers lived in huts built high in the branches and accessed by rope ladders hanging down during the day and drawn up at night. Between the huts was a system of rope bridges that connected them together, resembling a horizontal spider web of sorts. Justin loved walking back and forth across the bridges. The mango laden branches hung down as if offering up their fruit to the villagers. The villagers harvested the mangoes and placed the extra ones in a cart at the edge of the grove.
Although the Captain could sense there was little immediate danger, she could not ignore a nagging feeling of discomfort at the way Teena ignored her, the obvious leader of this group, in favor of Justin and her nephew, Jake. She found it odd that the oldest people in this tribe were in their early 20’s. They all seemed quite competent and even skillful in the way they took care of their village, but it was strange none the less.
The Captain tried to catch Teena’s attention several times to ask where the adults were. She had told Jake that she and Oto were the leaders of the tribe. But where were the parents, the younger kids and the grandparents? She couldn’t get a straight answer from Teena. Finally, she confided in Cynthia, Justin’s mother, about her worries that some terrible information was being withheld from them.

“You know something? I’ve been wondering the same,” said Cynthia quietly one day. “It’s like they are orphans or something. They are polite to me, to be sure, but they rarely talk to me about anything real. It’s almost as if they look straight through me when I am with them. I feel awkward asking them again.”

      “I’ve been thinking, why don’t we ask Justin and Jake? They seem to have an easier time talking with Teena.”

The boys were confused by the Captain’s request when she spoke with them later that day. They hadn’t noticed that Teena and Oto were basically ignoring the adults in favor of them. But now that they thought about it, they also began wondering about the adult villagers. They asked Teena about them.

“Oh, Adults are far, far away from here.”
“Why? Because that is the way of things. Adults live on the Rim and Youngsters live in the Grove. “
“Don’t you miss them?” asked Justin.
“Miss them? Why? We send them mangoes each month.”

Jake and Justin looked at each other.

“Adults are very busy people. We send them mangoes to help out and let them know we are ok.”
“How far away is the Rim?”
“It’s about 100 kilometers away. Our cart hold exactly 100 mangoes. When the Messengers are sent off with the mangoes, they have strict orders not to eat more than one mango per kilometer between the two of them. If they ate any less, though, they would die.” 

       Justin did a quick mental calculation and blurted, “Don’t they end up eating all the mangoes before arriving?”

“Oh, That is why we wait until we have 300 mangoes ready. We’ve developed a system of caches, sort of like holding bins, to leave mangoes along the way.  The Messengers go back and forth between the Grove and the different drop off points. At some point, they have collected all the mangoes they can at a certain drop off point and they set off to the Rim with their final load.”

“I’m confused,” said Jake. “How do the Messengers get back? 

Teena looked at him placidly, “Come back? Why would they do that?”

Your Task:  
Determine the maximum number of mangoes the Youngsters can get to the Adults on the Rim?

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