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Grid problem

Five children live in the town of Gridley which is represented by a grid of streets. On the x axis are the streets A, B and so on until Q. On the Y axis, the streets go from descending order from 15th Avenue down to 1st Avenue (in other words as you go up the Y axis, the avenues go down). So at the origin would be the intersection of A street and 15th Avenue (A, 15). Sally lives at the intersection of B and 4th. The other four children live at the following intersections:E and 14th, H and 5th, L and 13th and N and 14th. They have to meet to discuss homework but are lazy and insist on meeting at whichever intersection that would require the least amount of total travelling. All travelling must be along the lines on the map (no diagonal movement allowed.

A. Where should the five students meet?
B. Suppose Sally is not available, where should the other four meet?
C. All 33 students who live in Gridley decide to meet. How can they figure out the best spot once they have a map with the locations of all their homes?
D. What if all 350 people living in Gridley want to meet. How can they figure out where to meet?

Solution Preview

The correct way is: for either axis, say Y, you list the Y coordinates of all the students in an ascending sequence. If there are odd number of students, you just chose the Y coordinate in the middle as the Y coordinate of the meeting intersection. If there are even number of students, ...

Solution Summary

This shows how to arrange a meeting point so travel distance is minimized.

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