# Flowers in a circle Puzzle

Eight flowers, coded as A, B, C, D, E, F, G and H, are planted in a garden in the shape of a circle (not necessarily in that order). The flowers are of different types – Rose, Lotus, Daffodil, Sunflower, Daisy, Lilly, Dallion and Marigold, not necessarily in that order. The flowers are ranked in the descending order of their prices, rank 1 being the costliest, and no two flowers have the same price. The numeric sum of the ranks of any two flowers planted opposite to each other is odd. Further it is known that:

1. The costliest flower is not opposite to the cheapest flower, which, in turn, is Daffodil.

2. A, Sunflower, is the fourth costliest and is planted opposite to the flower which is fourth cheapest and which is Marigold.

3. Rose and Dallion are adjacent to each other.

4. B is opposite to C and one of them is Lilly and the other is Lotus.

5. Exactly one flower is planted between E and A. The flower planted opposite to E is Rose.

6. D is planted to the immediate right of A.The flower planted opposite to D is Daisy.

7. There is exactly one flower planted between F (which is the second cheapest flower) and the second costliest flower.

Show the arrangement and assignment of the flowers to their codes and flower type

• Are you positive this is solvable with only the hints you have given? – eye_am_groot Oct 30 '18 at 16:51
• What does "planted to the right of" mean? – Weather Vane Oct 30 '18 at 17:33
• D is adjacent to A. – sam Oct 30 '18 at 22:50

The best we can get from the current information:

(2) We know that Sunflower is A, ranked 4, and across from Marigold, ranked 5.
(6) D is to the right of A, making Daisy to the right of Marigold.
(5) Either E or Rose is two to the right of Sunflower (and the other is two to the left).
(4) Therefore, B or C (Lily/Lotus) is to the left of Sunflower, the other is to the left of Marigold.
(3) Dallion has to be to the right of Sunflower, making it D. Rose is adjacent to it.
(1) E is Daffodil and rank 8. Rose cannot be the most expensive.
(7) Rose cannot be ranked 2 or 7. Daisy must be F and ranked 7. Lily or Lotus must be ranked 2.
Using the sums: Rose must be 3, Dallion must be 6.

Order (clock-wise):

Sunflower $$\rightarrow$$ Lily/Lotus $$\rightarrow$$ Daffodil $$\rightarrow$$ Daisy $$\rightarrow$$ Marigold $$\rightarrow$$ Lily/Lotus $$\rightarrow$$ Rose $$\rightarrow$$ Dallion

Code:

A.Sunflower
B.Lily/Lotus
C.Lily/Lotus
D.Dallion
E.Daffodil
F.Daisy
G.Rose/Marigold
H.Rose/Marigold

Rank:

1.Lily/Lotus
2.Lily/Lotus
3.Rose
4.Sunflower
5.Marigold
6.Dallion
7.Daisy
8.Daffodil

Assuming I am correct so far, I don't know:

Where B and C are, which is Lily, which is Lotus and which is the most expensive and second most expensive.
Is Marigold or Rose G and H.

• I'm running into the same roadblocks as you. Not sure if there is enough information to get a definite answer. – Robert S. Oct 30 '18 at 16:45
• @RobertS. as there is no mention of two of the letters I am (we are?) missing, I am starting to think we can't. – eye_am_groot Oct 30 '18 at 16:49
• +1, same boat here. – user41531 Oct 30 '18 at 16:52
• I had "right of A" as looking from the inside of the circle, so mine is the other way around. – HollyLeaves Oct 30 '18 at 17:37
• @HollyLeaves interesting! I was looking down on it from the sky, but I could see your way too – eye_am_groot Oct 30 '18 at 17:40

I think there are 32 ways for this to be possible

My approach: Process of elimination

Table and a diagram:

Explanation of the table and diagram:

You can use the process of elimination/logical deduction to find four flowers and their letter along with rank.The pencil-circled ones in the diagram show these four flowers.

The flowers Marigold and Rose have exact ranks 5 and 3 respectively,but their letters needn't be exact.If any one of them has letter G then the other will have H and vice versa.

B and C,each can have ranks either 1 or 2 and moreover in each case they can either be lotus or Lilly.

Conclusion:

There will be a total of 32 possibilities based on the hints you've provided

• Hi @ayc. Be sure to hide your answer using ">!" – eye_am_groot Oct 30 '18 at 17:31
• Also, I answered the same thing :-) – eye_am_groot Oct 30 '18 at 17:32
• @Greg..Actually I figured it out too,on my own.I have given my answer although your's exists because I thought it would be easier to understand in the way I've answered rather than yours as your's will take time to get organized in the mind. – ayc Oct 30 '18 at 17:37
• No problem, just saying we had the same idea (didn't think you'd just repost my answer) – eye_am_groot Oct 30 '18 at 17:39