Monday, November 14, 2011

Quick Logic on Bees and Flowers

In a pond there are some flowers with some bees hovering over the flowers. How many flowers and bees are there if both the following statements are true:

1. If each bee lands on a flower, one bee doesn’t get a flower.
2. If two bees share each flower, there is one flower left out.


  1. I think there are 7 bees and flowers.

  2. 4 bees, 3 flowers.

    3 bees land on 3 flowers, and one doesn't get a flower.

    2 bees land on 2 flowers (4 bees total), and 1 flower gets left out.

    Mathematically, the two statements can be expressed:
    1. f = b-1
    2. b/2 + 1 = f

    #1 states that the number of flowers is equivalent to the number of bees minus one.

    #2 states that the number of flowers is going to be equal to half the bees (because two are on each flower) plus one left over.

    Put the two equations together and you can solve for b or f.

  3. 4 bees and 3 flowers
    ( )

  4. You both got it, four bees and three flowers.


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