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Puzzle ZROR 



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Gardener's Spring Fayre - Logic Puzzles

At the recent spring fayre, 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?

Gardener Green had a yellow rose.
Gardener Yellow did not have a red one.
Gardener Red had a blue rose, but not a green one.
Gardener 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 had two roses of the same colour.
No two persons had the same two colour roses, and their names provide no clues.

Puzzle Copyright © Kevin Stone

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Answer
Name
   Rose1
      Rose2


Gardener Blue
   red
      green

Gardener Green
   yellow
      red

Gardener Red
   blue
      yellow

Gardener Yellow
   blue
      green

Reasoning
We can create a grid of the possible flowers each person 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 reduce 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

 

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