math

Consider an equilateral triangle with points located at each vertex and at each midpoint of a side. (See picture.) This problem uses the set of numbers {1, 2, 3, 4, 5, 6}. Place one number at each point. Call the sum of the three numbers along any one side (two vertices and one midpoint) a “Side Sum.” There are arrangements of the numbers so that the sum of the numbers along any side is equal to the sum of the numbers along each of the two other sides. We will call this arrangement an Equal Side Sum solution.
1) Show that more than one Equal Side Sum solution exists.
a. For which numbers are Equal Side Sum solutions possible? (Show by giving examples for each Equal Side Sum solution that is possible.) Comment on how you obtained these solutions.
b. What is the smallest number for which there is an Equal Side Sum solution? Why?
c. What is the largest number for which there is an Equal Side Sum solution? Why?
2) Is there more than one Equal Side Sum solution for the same number? (To answer this question, you will need to be precise as to what you mean when you say that two Equal Side Sum solutions are the same or are different.) Explain your answer.
Extra Credit: It is possible to generalize The Triangle Game to create a similar game involving other polygons. Describe such a game. Are you able to find any solutions to your new game? Worth up to two extra credit points

  1. 1
asked by al
  1. Two whole numbers are less than 10 and grèater than 0.whats the difference between their product and their sum.

    posted by Josh

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    An equilateral triangle initially has side length equal to 17 cm. Each vertex begins moving in a straight line towards the midpoint of the opposite side at a constant rate of 2.3 cm/s, continuously forming progressively smaller
  2. geometry

    Theres a circle with an equilateral triangle in the middle. The traingles edges all touch the circle. The radius of the circle is 8 meters. How do I find the area of the triangle? Sorry The triangles edges don't touch the circle,
  3. Analytic Geometry

    The line segment joining a vertex of a triangle and the midpoint of the opposite side is called the median of the triangle. Given a triangle whose vertices are A(4,-4), B(10, 4) and C(2, 6), find the point on each median that is
  4. corollary to isosceles triangle theorem

    how to prove 1)the measure of each angle of an equilateral triangle is 60. 2)the bisector of the vertex angle of an isosceles triangle is the perpendicular bisector of the base. Thanks. 1) The angles in any triangle have to add up
  5. geometry

    An equilateral triangle ⌂ABC has two of its vertices below the x-axis, has the third vertex C above the x-axis, and contains the points A=(0,0)and B=(1,0) on its sides. How long is the path traced out by all possible points C,
  6. Algebra--please help!

    Here are some more questions I'm having trouble with. Please walk me through them so I can fully understand them. #2: Let A be (5,9), B be (-3,-5), and C be (1,1). The median of a triangle connects a vertex of a triangle to the
  7. maths

    An equilateral triangle is inscribed in parabola y^2=4axsuch that the vertex of the triangle is at vertex of parabola find area of triangle
  8. General Physics II

    ___A __/__\ B/____\C radius (each side of this equilateral triangle) 0.5 m Three point charges are located at the corners of an equilateral triangle as in the figure below. Find the magnitude and direction (counterclockwise from
  9. Math

    An equilateral triangle is one in with all three sides are length. If two vertices of an equilateral trangle (0,4) and (0,0), find the third vertex. How mant of these triangles are possible? How would you slove this??
  10. Calc HELP!

    an equilateral triangle is one in with all three sides are length. If two vertices of an equilateral trangle (0,4) and (0,0), find the third vertex. How mant of these triangles are possible? How would you sove this???

More Similar Questions