The new walled section of the city was finally complete. The five sects that dominated the city, Fire, Sun, Light, Earth, and Ice, had plans to abandon their humble places of worship outside the city walls. The five had chosen the sites for their grandiose temples inside the new section of the city. The city’s overseer, Mayor Templeton, didn’t want to hand over too much of his new area to the sects, but he was wary of the power they held over the people.
Each sect had been given their own specialized gate into the new walled section, and each demanded that a roadway, one square wide, be made from their respective gate to the individual temples, that their followers would use at high noon every day. The sects further demanded that the way should be unobstructed by followers of a different sect. None of the roadways could cross.
Mayor Templeton said he would give the sects what they wanted, but only if at least half of the blocks inside the new section could be used for the people’s other needs, like housing, marketplaces, and civic centers. If half or more of the sections area were left available after the sects had built their temples and roadways, the Mayor would comply with their demands, and all agreed.
The city planners were stumped, however. They could not figure out how to lay out the roads so that none crossed and still leave enough blocks left over to meet the Mayors needs as well. They finally determined to turn to outside help to try to solve the problem.
Will you help?
Can the roads from the gates to the corresponding temples be built in such a way that they don’t take up more than half of the new sections area (when combined with the area of the new temples)?
If it can be done, than how?
256 = Total blocks
128 = ½ the Total blocks
20 = Blocks taken by the temples
108 = Number of blocks that all the roads cannot exceed
Question
Prof. Templeton
The new walled section of the city was finally complete. The five sects that dominated the city, Fire, Sun, Light, Earth, and Ice, had plans to abandon their humble places of worship outside the city walls. The five had chosen the sites for their grandiose temples inside the new section of the city. The city’s overseer, Mayor Templeton, didn’t want to hand over too much of his new area to the sects, but he was wary of the power they held over the people.
Each sect had been given their own specialized gate into the new walled section, and each demanded that a roadway, one square wide, be made from their respective gate to the individual temples, that their followers would use at high noon every day. The sects further demanded that the way should be unobstructed by followers of a different sect. None of the roadways could cross.
Mayor Templeton said he would give the sects what they wanted, but only if at least half of the blocks inside the new section could be used for the people’s other needs, like housing, marketplaces, and civic centers. If half or more of the sections area were left available after the sects had built their temples and roadways, the Mayor would comply with their demands, and all agreed.
The city planners were stumped, however. They could not figure out how to lay out the roads so that none crossed and still leave enough blocks left over to meet the Mayors needs as well. They finally determined to turn to outside help to try to solve the problem.
Will you help?
Can the roads from the gates to the corresponding temples be built in such a way that they don’t take up more than half of the new sections area (when combined with the area of the new temples)?
If it can be done, than how?
256 = Total blocks
128 = ½ the Total blocks
20 = Blocks taken by the temples
108 = Number of blocks that all the roads cannot exceed
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