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

In total there were four colours and each rose colour appeared twice.

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

QED.

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