A grove of 52 trees is arranged in circular fashion. if 15chipmunks live in thes

Question

A grove of 52 trees is arranged in circular fashion. if 15chipmunks live in these trees, show that thre is a group of 7consecutive trees that together house at least 3 chipmunks. Discuss, in detail, how the solution will be different ifthe 52 trees in the "chipmunks" problem (Example 2r in Chapter 7)are arranged on a straight line rather than arranged on acircle. A grove of 52 trees is arranged in circular fashion. if 15chipmunks live in these trees, show that thre is a group of 7consecutive trees that together house at least 3 chipmunks. Discuss, in detail, how the solution will be different ifthe 52 trees in the "chipmunks" problem (Example 2r in Chapter 7)are arranged on a straight line rather than arranged on acircle. A grove of 52 trees is arranged in circular fashion. if 15chipmunks live in these trees, show that thre is a group of 7consecutive trees that together house at least 3 chipmunks. Discuss, in detail, how the solution will be different ifthe 52 trees in the "chipmunks" problem (Example 2r in Chapter 7)are arranged on a straight line rather than arranged on acircle.

Explanation / Answer

Assuming the chipmunks are equally spaced: 52 trees/15chipmunks = 3.46666... trees/chipmunk
If the trees are arranged in a circle then you will have:
...chipmunk_3.47 trees_another chipmunk_3.47 trees_anotherchipmunk...etc
so the total number of trees is 2*3.466666... = 6.9333... trees for3 chipunks. Since that is less than 7 there should be at least 3chipmunks in 7 trees.
If the trees are in a line instead of a circle then at the end ofthe line there could be
end_3.47 trees_chipmunk_3.47 trees_chipmunk so you could have only2 chipmunks in 7 trees

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