Digit Puzzle
What four digit number has...
...digit 2 smaller than digit 4 which is two thirds of digit 1 which is two thirds of digit 3 which is three times digit 2?
Solution (Previous Puzzle):
Name Rose1 Rose2
Gardener Blue red green
Gardener Green yellow red
Gardener Red blue yellow
Gardener 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. Gardener Green had a yellow rose (1). Gardener Yellow did not have a red one (2). Gardener Red had a blue rose but not a green one (3), whilst Gardener 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 had 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 had 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
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