Solve The Puzzle: Which Gardener Had Which Colors Of Roses?

At the recent spring fete, four keen gardeners were displaying their fine roses.

In total there were four colours of roses (red, green, yellow and blue) and there were two roses from each colour.
Every gardener brought two roses. None of the gardeners brought roses from same colour and there were no same combination of rose colours.

From the clues below can you tell who had which colour roses?

1. Mr Green had a yellow rose.
2. Mr Yellow did not have a red one.
3. Mr Red had a blue rose but not a green one.
4. Mr Blue did not have a yellow one.
5. One person with a red rose also had a green one.
6. One person with a yellow rose also had a blue one.
7. One of the persons with a green rose had no red.
8. Neither of the persons with a yellow rose had a green one.
9. No person has two roses of the same colour.
10. No two persons had the same two colour roses and their names provide no clues.

Below is the hint and the answer, but it is more fun and brings satisfaction of you can solve it by yourself 🙂
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HINT!

Draw a grid of the two colours each gardener could have.

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Answer:

[ultimatetables 2 /]

Solution:

In total there were four colours of roses (red, green, yellow and blue) and there were two roses from each colour.
Mr Green had a yellow rose (1).
Mr Yellow did not have a red one (2).
Mr Red had a blue rose but not a green one (3), whilst Mr Blue did not have a yellow one (4).
One person with a red rose also had a green one (5).
One person with a yellow rose also had a blue one (6).
One of the persons with a green rose had no red (7).
Neither of the persons with a yellow rose had a green one (8).
No person has two roses of the same colour (9) and no two persons had the same two colour roses (10) and their names provide no clues.
Can you tell who had which colour roses?

Firstly we label the clues. If we now create a grid for each person that has the two possible flowers they could have. Initially they each have the possibility of BGRY (blue, green, red, yellow) and as we work our way through the clues we can eliminate certain options.

Person F1 F2
Blue BGRY BGRY
Green BGRY BGRY
Red BGRY BGRY
Yellow BGRY BGRY

From (1), (2), (3) and (4) we can reduced the options to:

Blue BGR BGR
Green Y BGRY
Red B BRY
Yellow BGY BGY

By (9) this becomes:

Blue BGR BGR
Green Y BGR
Red B RY
Yellow BGY BGY

By (8) we get:

Blue BGR BGR
Green Y BR
Red B RY
Yellow BGY BGY

Only Blue can satisfy (5), and Yellow is the only person who can have the other G.

Blue R G
Green Y BR
Red B RY
Yellow G BY

By (8), Yellow can’t be Y.

Blue R G
Green Y BR
Red B RY
Yellow G B

Since there are only two of each colour, we can reduce further:

Blue R G
Green Y R
Red B Y
Yellow G B