Friday, October 2, 2009

Beds of Flowers




Dona and Dennis have a large yard and are thinking of putting in some new flower beds. Dennis went to the local garden center and came home with the following plants:







When Dona saw the flowers, she made the following requests for the beds.


  • The same type of flowers could not be in the same bed.
  • The same color of flowers could not be in the same bed.


  • How many beds will Dennis have to dig?
  • What types and colors will go in each bed?


Describe, in detail, how you solved this problem.

25 comments:

  1. Dennis will have to dig 3 beds.
    #1: Yellow Marigolds, Purple Cosmos, Pink Zinnias.
    #2: Yellow Asters, Pink Cosmos, White Zinnias.
    #3: Yellow Zinnias, Pink Asters, White Asters, Orange Marigolds.

    --C.A.

    ReplyDelete
  2. S.G.

    - Ben will dig up 3 beds.

    -1 bed: Yellow Marigolds, Purple Cosmos, White Zinnias, and Pink Asters.
    2 beds: Orange Marigolds, Pink Cosmos, Yellow Zinnias, and White Asters.
    3 beds: Pink Zinnias, and Yellow Asters.

    ReplyDelete
  3. E.D.
    Answer:
    Dennis will have to dig 3 beds of flowers with these types and colors:
    Bed 1- Yellow Marigolds, Purple Cosmos, White Zinnias, Pink Asters
    Bed 2- Orange Marigolds, Pink Cosmos, Yellow Zinnias, White Asters
    Bed 3- Pink Zinnias, Yellow Asters

    ReplyDelete
  4. MNH
    1. He would have to dig 3 beds.
    2. Bed 1: Yellow Marigolds
    Purple cosmos
    Pink Zinnias
    White Asters
    Bed 2: Orange Marigolds
    Pink Asters
    Yellow Zinnias
    Bed 3: White Zinnias
    Yellow Asters
    Pink Cosmos


    I solved this problem by listing all the types and colors of flowers and sorting them into groups without using the same type of flower or the same color of flower in each bed.

    ReplyDelete
  5. HB
    1. He would have to dig 3 beds.
    2. Bed 1: Yellow Marigolds, Purple Cosmos, Pink Zinnias, White Asters.
    Bed 2: Orange Marigold, Pink Aster, Yellow Zinnias.
    Bed 3: White Zinnias, Pink Cosmo, Yellow Aster.


    The way I solved this problem is by listing all the different colors and types of flowers into different groups without using the same color or type of flower in the same bed.

    ReplyDelete
  6. S.A
    Bed 1 Yellow Marigolds, purple comos, pink Zinnias, White asters
    Bed 2 Orange Marigolds, Pink comos, white zinnias yellow asters
    Bed 3 Yellow zinnias, pink asters

    I solved this buy stating with the 1st flower and had that be a bed and then went down the list and witch ever one fit the rules I put that one in the 1st bed. The I took a flower that did not fit in the 1st bed made that a bed then again went down the list and put witch ever one sit in the second bed I put it in there. Then there was two flowers left who could not fit in either bed so I put them in another bed.

    ReplyDelete
  7. JD
    #1 He would have to dig 3 beds.

    #2 Bed 1: yellow marigolds, purple cosmos, white zinnias, pink asters

    Bed 2: orange marigolds, pink cosmos, yellow zinnias, white asters

    Bed 3: pink zinnias, yellow asters

    I solved this problem by listing the colors of flowers and the types of flowers in groups. In the groups I made sure they followed the guide lines of the problem.

    ReplyDelete
  8. SR
    bed 1 bed 2 bed 3
    ym om yz
    ppc pkc wa
    wz ppz
    pka ya
    I listed all the combinations. Then want thought and put them all in boxes.
    This is my key
    Ym= yellow marigolds
    Om= orange marigolds
    Ppc= purple cosmos
    Pkc=pink cosmos
    Wz= white cosmos
    Pkz= pink zinnias
    Yz= yellow zinnias
    Pka=pink asters
    wa= white asters
    ya= yellow asters

    ReplyDelete
  9. JS
    #1 Dennis will have to dig three beds.

    #2 In bed 1 there will be yellow marigolds, purple cosmos, white zinnias, and pick asters.

    In bed 2 there will be orange marigolds, pink cosmos, yellow zinnias, and white asters.

    In bed 3 there will be pink zinnias and yellow asters.

    I solved this problem by writing out all the different groups and making sure I didn’t put duplicate colors or types. Then I counted how many groups there was and I counted three so the answers is three.

    ReplyDelete
  10. The flower beds
    Yellow Marigolds, Yellow Zinnias, Yellow Asters
    Orange Marigolds
    Pink Cosmos, Pink Zinnias, Pink Asters
    White Zinnias and White Asters

    There would be 3 flower beds
    In the beds are…
    Yellow Marigolds and Purple Cosmos White Zinnias and Pink Asters
    , bed 1
    Orange Marigolds, Pink Cosmos, Yellow Zinnias, and white Asters, bed 2
    Pink Zinnias and Yellow Asters.

    I sorted out the colors first, then I figured out what groups could go with each other, then I decided if the colors were correct, and if it met the correct criteria I would put it in a group that didn’t have the same color or same type of flower.

    ReplyDelete
  11. M.W.
    Dennis and Dona will have 3 beds to plant.

    First I abbreviated the plant names so they were easier to work with:
    Y m
    O m
    Pu c
    Pi c
    W z
    P z
    Y z
    P a
    W a
    Y a

    There were 6 colors, 4 different kinds of flowers, and 10 different flowers.

    The first bed would have Yellow Marigolds, Purple Cosmos, White Zinnias, and Pink Asters. The second bed would have Orange Marigolds, Pink Cosmos, Yellow Zinnias, and White Asters. The third bed of flowers would have only two flowers. It has Pink Zinnias and Yellow Asters. I got these combinations by listing out the flowers and crossing out the ones I was sure were in the right group. I went over the groups I had making sure they didn’t have the same color or kind in their bed.

    ReplyDelete
  12. MO
    Ym
    Om
    Puc
    Pic
    Wz
    Pz
    Yz
    Pa
    Wa
    Ya

    Om, pic, wz, ya
    Ym, puc wa, pz
    Yz, pa

    First I abbreviated the flowers names. Then I started putting them into groups, making sure I didn’t have the same kind or color of flower in the same bed. The first bed would have Orange Marigolds, Pink Cosmos, White Zinnias, and Yellow Asters. The second bed will have Yellow Marigolds, Purple Cosmos, White Asters, and Pink Zinnias. The final flower bed will only have two flowers which are: Yellow Zinnia and Pink Asters. I found my answer by putting them into groups and organizing them by color and flower. As in, to make sure I didn’t put the same colors in, or the same flowers. My friend who sits next to me worked alone and still figured out the answer which was the same as mine. So, in conclusion, Dennis needs to make 3 flowerbeds.

    ReplyDelete
  13. J.V

    Dennis will have to dig three flower beds.

    Bed 1: Yellow, Purple, Pink, and White.
    Bed 2: Yellow, and Pink.
    Bed 3: Yellow, Orange, Pink, and White.
    Bed 1 Bed 2 Bed 1

    ReplyDelete
  14. Dennis will have to use three flower beds.

    In bed one he will have four different types of flowers in all different colors.
    In bed two he will have two different types of flowers in all differnt colors.
    In bed three he will have four differnt types of flowers in all different colors.


    R.N.W.

    ReplyDelete
  15. Dennis will have to dig three beds for the flowers.
    In one bed, there are 4 different flowers, all different colors. In another bed there are also 4 different flowers, all different colors. In one of the beds there are 2 different flowers, both different colors.

    ReplyDelete
  16. P.M.

    To figure out the problem I started by putting all the different flowers in a list. Next, I used lines to connect them to pick which beds they would go in. I then made a list of the beds and their contents.

    Bed 1: yellow marigolds, pink cosmos, and white zinnias

    Bed 2: orange marigolds, purple cosmos, pink zinnias, and white asters

    Bed 3: yellow zinnias and pink asters

    Bed 4: yellow asters

    Based on this list, there are four beds. Notice no same types of flowers or same color flowers are in the same bed.

    ReplyDelete
  17. N.H.

    Dennis will have to dig 4 beds. This is because the only way that the flowers can follow Dona’s criteria is to be in the following beds.
    Bed 1: Yellow marigold, pink cosmo, and white zinnia.
    Bed 2: Orange marigold, purple cosmos, pink zinnias, and white asters.
    Bed 3: Yellow zinnias, and pink asters.
    Bed 4: A yellow asters.
    Notice that in all of these none of them are ever the same color, or the same type of flower.

    ReplyDelete
  18. JS

    Dennis will have to dig three beds. You can prove that by looking at the table and seeing that three correct beds were needed.
    For the types and colors of each bed refer to the table. I got the information on the table by getting a list of all the flowers and sorting them so each bed does not have the same type of flower or color.

    ReplyDelete
  19. M.D.

    To solve this problem, I first wrote down on a piece of paper that there are four different types of flowers and five different flowers. Then, I drew a box to represent one bed. I wrote down all of the flower types and their colors. In one box, I listed first the yellow marigolds for flower bed one. Then, in the same bed, purple cosmos. After that, I added pink zinnias and white asters. In the second flower bed, there were yellow asters, pink cosmos, orange marigolds, and white zinnias. In the third and last bed, there would be yellow zinnias and pink asters. That is the order to have the least amount of flower beds.

    ReplyDelete
  20. bs
    1. Dennis will have to dig at least 3 beds. I figured this out by trying different combinations of flowers in the beds. I knew that there had to be at least 3 because there are 3 yellow flowers and 3 pink flowers and since the same color cannot be in the same bed, there have to be at least 3 beds. Then I tried putting the types and colors in different beds and got a combination that only uses three beds.

    2. This was the combination I came up with:
    bed 1:yellow marigold, purple cosmos, pink zinnias, and white asters.
    bed 2:orange marigolds, pink cosmos, white zinnias, and yellow asters.
    bed 3:yellow zinnias,and pink asters.

    ReplyDelete
  21. S.S.
    I figured this problem by writing down each combination of flowers and colors and then, on a piece of paper I drew a box. I looked at the list of flowers and colors and started off by making one bed. I put in yellow marigolds, purple cosmos, pink zinnias, and white asters. I made a second bed with yellow zinnias, orange marigolds, and pink asters. The third one had yellow asters and pink zinnias. The last one had white zinnias.

    ReplyDelete
  22. B.H.
    I figured this problem out by first putting all the pink flowers in three different flower beds. Then I added one yellow flower to each of the flower beds. Then I added the two white flowers to two of the three flower beds. Then I added the one orange flower to one of the three flower beds. Finally I put the one purple flower in one of the three flower gardens. I knew to do this because the most amount of one color flower is three. The most amount of one type of flower is three.

    ReplyDelete
  23. MH
    Dennis would have to dig 3 beds.

    1 would have Yellow Marigolds, Purple Cosmos, White Zinnias, and Pink Asters.

    2 would have Orange Marigolds, Pink Cosmos, Yellow Zinnias, and White Asters.

    3 would have Pink Zinnias and Yellow Asters.

    I wrote everything on a piece of paper, wrote a number next to it and made each number a list.

    ReplyDelete
  24. JR
    The first thing I did was list all of the types and colors of the flowers on a shhet of paper.Then I sorted them out so I could have the requierments that Dona had. I sorted them into three boxes:
    Box 1: YellowMarigold PurpleCosmo PinkZinnia WhiteAster
    Box 2: OrangeMarigold PinkCosmo WhiteZinnia YellowAster
    Box 3: YellowZinnia PinkAster
    Dennis will have to dig 3 boxes.

    ReplyDelete
  25. Z=Zinnias
    C=Cosmos
    M=Marigolds
    A=Asters

    Describe, in detail, how you solved this problem.

    All I did was follow the requirements given by the wife and switched from Purple C to Orange M so that each time the bed had 4 flowers.

    Bed 1 Bed 2 Bed 3
    Yellow Z Yellow M Yellow Z
    Purple C White Z Orange M
    Orange M Purple C Pink C
    Pink A Pink A White A

    ReplyDelete