Bosco

There are four cities: Capital City, Little Village, Mytown, and Yourtown.  The distance from Capital City to Little Village is $5$ miles.  The distance from Capital City to Mytown is $2$ miles.  The distance from Mytown to Yourtown is $3$ miles.  The distance from Little Village to Yourtown is $4$ miles.  Find the distance from Capital City to Yourtown, in miles.   

Little Village ----- 4 ----- Your Town ----- 1 ----- Capital City ----- 2 ----- My Town   

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Only 1 triangle is possible, and its side lengths are 1-1-1.  

Any other triangle with that perimeter won't have integer sides.  

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Combinations           Permutations    

1  2  2  2  5  5             ₆P₆ = 720    

1  1  2  4  5  5             ₆P₆ = 720    

total possible sequences    1440    

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Only 1 triangle is possible, and its side lengths are 1-1-1.  

Any other triangle with that perimeter won't have integer sides.  

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A rectangular room measures 12-feet by 6-feet. How many square   

yards of carpet are needed to cover the floor of the room?  

    12 ft       1 yd   

    ––––  x  –––––  =  4 yd    

       1          3 ft    

     6 ft        1 yd   

    ––––  x  –––––  =  2 yd    

       1          3 ft    

       4 yd  x  2 yd  =  8 yd²

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