Let the number of Rose plants be

**a**.

Let number of marigold plants be

**b**.

Let the number of Sunflower plants be

**c**.

According to question,

20a + 5b + 1c = 1000 - - - - - - (1)

a + b + c = 100 - - - - - - - - - - (2)

Solving the above two equations by eliminating c, 19a + 4b = 900

b = $$\frac{{900 - 19a}}{4}$$ = $$225 - \frac{{19a}}{4}$$ - - - - - - - (3)

b being the number of plants, is a positive integer, and is less than 99, as each of the other two types have at least one plant in the combination i.e .

0 < b < 99 - - - - - - - (4)

Substituting (3) in (4),

0 < 225 - $$\frac{{19a}}{4}$$ < 99

⇒ 225 < -$$\frac{{19a}}{4}$$ < (99 - 225)

⇒ 4 × 225 > 19a > 126 × 4

⇒ $$\frac{{900}}{{19}}$$ > a > 504

a is the integer between 47 and 27 - - - - - - - - (5)

From (3), it is clear, a should be multiple of 4.

Hence, possible values of a are (28,32,36,40,44)

For a=28 and 32, a+b>100

For all other values of a, we get the desired solution:

a=36,b=54,c=10

a=40,b=35,c=25

a=44,b=16,c=40

Three solutions are possible.