Peter Piper
Alan Ardman
Zach Zebra
Frank Flintbone
Matthew Merryman
Jimmy James
Graham Goodfellow
Tom Trent
Brian Brick
Kevin Kingfisher

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

Three. If the ogre pulled out only two
boots, he might have had to wear one six-league and one
seven-league boot. He took out three because at least two
of the three would have to be the same type. The formula:
N + 1 (N represents the number of types). 2 + 1 = 3.

Four. The formula again: N + 1 (with N
representing the types of ogre-fighters). If the swordsmith
had pulled out two or three, he might have picked one of
each type. Since he had only three types of weapons, with
four he would have at least two of one type. He had three
types of weapons and so N = 3. 3 + 1 = 4.

Ten. Though, by chance, she might
have taken down four matching plates, consider the possibilities
if the queen had taken down the following
number of plates:
4 might have resulted in 2, 1, 1
5 might have resulted in 2, 2, 1
6 might have resulted in 2, 2, 2
7 might have resulted in 3, 2, 2
8 might have resulted in 3, 3, 2
9 might have resulted in 3, 3, 3
Only with ten, would it be inevitable that she would
have at least four of any one pattern: 3, 3, 4.
In order to ensure matching plates, the queen had to
bring down three extra plates, one for each pattern, for
each person more than two.
The formula: N + 1 + N(X) (with N representing the
number of patterns or types and X representing the
number of people more than two).
The queen had three patterns of plates and so N = 3. In
addition to the king and queen, there were two guests,
and so X = 2. 3 + 1 + 3(2) = 10.
Try it and you will find that for three persons the queen
would have needed to take down seven plates, and for five
she would have had to take down 13 plates.
If her children had not been out ogre-fighting, the royal
queen might have had to mix and match!

Anti-Ogre Potions: Seven. If the wizard took out four
potions, he certainly would have two of the same kind, but
not necessarily the ogre-fighters. He could have two of the
evil wizard-vanquishers or the dragon-destroyers. And
what good would they be in combat with an ogre?
If he took out five potions, he might wind up with three
dragon-destroyers, two evil wizard-vanquishers, and no
ogre-fighters. If he grabbed for six potions, they might
include three dragon-destroyers, two wizard-vanquishers,
and one ogre-fighter. But if he took out seven, he would
have to have at least two ogre-fighters, since only five
other potions are not ogre-fighters.

Six. Since he had only four sixleague
boots, if he took out six boots, he’d have at least one
pair of seven-league boots.

Prince Benjamin. We know that Sir Kay shot down more than Princess Paula (statement 1), and that Prince Benjamin captured more than Sir Kay (statement 2).
Therefore, Prince Benjamin captured more than either Sir Kay or Princess Paula.
In addition, we know that Princess Paula hit more than Prince Abel (statement 3). Therefore, Prince Benjamin was more successful than Sir Kay, Paula or Abel.

1. Uti finned and Uti feathered swung over.
2. Uti finned returned.
3. Grundi feathered and Grundi finned swung over.
4. Uti feathered returned.
5. Yomi feathered and Yomi finned swung over.
6. Grundi finned returned.
7. Uti feathered and Uti finned swung over.
8. Uti finned returned.
9. Uti finned and Grundi finned returned.

1. One Earthling took one Grundi across (leaving two
Earthlings and two Grundi on the west side).
2. One Earthling returned (leaving one Grundi east).
3. Two Grundi crossed (leaving three Earthlings west).
4. One Grundi returned (leaving two Grundi east).
5. Two Earthlings crossed (leaving one Grundi and one
Earthling on the west).
6. One Grundi and one Earthling returned (leaving one
Grundi and one Earthling on the east side).
7. Two Earthlings crossed (leaving two Grundi west).
8. One Grundi returned (leaving three Earthlings east).
9. Two Grundi crossed (leaving one Grundi west).
10. One Grundi came back (leaving three Earthlings and
one Grundi on the east side).
11. Two Grundi crossed (no one left in danger).
10. Fins and Feathers:
1. Uti finned and Uti feathered swung over.
2. Uti finned returned.
3. Grundi feathered and Grundi finned swung over.
4. Uti feathered returned.
5. Yomi feathered and Yomi finned swung over.
6. Grundi finned returned.
7. Uti feathered and Uti finned swung over.
8. Uti finned returned.
9. Uti finned and Grundi finned returned.
11. Flying Teams: Wora and Pyi.
1. From statement 6, we can assume that Xera and Rir
come from different groups since they would have
known one another if they were on the team from the
same group.
2. From statement 7, we learn that Xera is a Yomi.
3. Therefore neither Rir, who comes from another group,
nor Pyi, whom she will visit, comes from Yomi territory.
4. Since each team has one male on it, Vel, the only one
left, must be the male who is a Yomi
5. Since Xera is a Yomi, either Teta or Wora must be the
female on the Uti team.
6. But, from statements 5 and 8, we learn that Teta’s home
is the land of the Grundi.
7. Two Earthlings crossed (leaving two Grundi west).
8. One Grundi returned (leaving three Earthlings east).
9. Two Grundi crossed (leaving one Grundi west).
10. One Grundi came back (leaving three Earthlings and
one Grundi on the east side).
11. Two Grundi crossed (no one left in danger).