# Find the roses

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

In total there were four colours and each rose appeared in two colours.

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

- Mr Green had a yellow rose.
- Mr Yellow did not have a red one.
- Mr Red had a blue rose but not a green one.
- Mr Blue did not have a yellow one.
- One person with a red rose also had a green one.
- One person with a yellow rose also had a blue one.
- One of the persons with a green rose had no red.
- Neither of the persons with a yellow rose had a green one.
- No person has two roses of the same colour.
- No two persons had the same two colour roses and their names provide no clues.

__Name Rose1 Rose2__

Mr Blue red green

Mr Green yellow red

Mr Red blue yellow

Mr Yellow blue green

At the recent spring fete, four keen gardeners were displaying their fine roses. In total there were four colours and each rose appeared in two colours. 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

### Your Answer

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