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