Equal-Sum Groups

Problem Set I

Separate each group of numbers into TWO smaller groups so that the sum of the numbers in each of the small groups is the same. NOTE: there may be more than one way to do a problem. If so, can you find the other ways?

a)  {3, 7, 9, 13}        f)  {5, 9, 10, 13, 19}

b)  {2, 3, 4, 7, 10}        g)  {1, 2, 7, 12, 23, 31}

c)  {2, 4, 7, 9, 10}        h)  {1, 3, 4, 6, 8, 12, 13, 15, 16}

d)  {1, 4, 5, 6, 9, 13}    i)  {3, 9, 13, 16, 28, 37}

e)  {5, 8, 9, 10, 12}

Problem Set II

Separate each group of numbers into THREE smaller groups so that the sum of the numbers in each of the small groups is the same. NOTE: again, there may be more than one way to do a problem. If so, can you find the other ways?

a)  {2, 3, 4, 8, 9, 10, 14, 17, 26}

b)  {4, 5, 6, 7, 8, 19, 21, 22, 28}

c)  {3, 4, 8, 9, 11, 15, 19}

d)  {2, 5, 7, 8, 11, 14, 15, 16}

e)  {1, 3, 4, 10, 12, 14, 15, 16, 17, 18, 23, 26}

f)  {4, 6, 7, 9, 12, 14, 17, 23 25}

g)  {1, 2, 4, 8, 11, 12, 15, 19, 36}

Problem III

Make up a problem or two like these to share with your classmates. Just be careful that it does have at least one solution.

Teacher’s Note: In problem set I there are two solution methods for two groups [d and i] and six solutions for group “h”.

In problem set II groups a, b, f, and g have two solutions each, and group e has at least 13 (!) different ways to be solved.

tt(1/3/77)

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