Mathematical Puzzle

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.
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.
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You are trying to cook an egg for exactly fifteen minutes, but instead of a timer, you are given two ropes which burn for exactly 1 hour each. The ropes, however, are of uneven densities – i e , half the rope lengthwise might take only two minutes to burn. How can you cook the egg for exactly fifteen minutes?
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On Bagshot Island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel.
What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? How did you get to your answer?Notes:
(a) Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.
(b) Each airplane must have enough fuel to return to airport.
(c) The time and fuel consumption of refueling can be ignored. (so we can also assume that one airplane can refuel more than one airplanes in air at the same time.)
(d) The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes. What is the fewest number of airplanes and number of tanks of fuel needed to accomplish this work? (we only need airplane to go around the world)View SolutionSubmit Solution 7191 views
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You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You’ve got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.
You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.
You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.
What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
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On the day before the spacecraft was to return to
Earth, the Martians held a dinner party for the crew. In
all there were eight at the table: Aken, Bal, Mun, Mark,
Wora, Jones, Rider and Smith.
a. One was a history buff.
b. One was a whiz at math.
c. One was very tall.
d. One was Aken’s friend.
e. One had yellow feathers.
f. One was a pilot.
g. One was a rock collector.
h. One spoke a number of languages.
1. The person who was Aken’s friend sat directly
opposite Mark.
2. Wora sat between the math whiz and Aken’s
friend.
3. The tall one sat opposite Wora, with Aken to her
left.
4. Smith, who had no real friends among the group,
sat to the right of Mun who towered over the rest
of the group.
5. The one who had yellow feathers sat opposite Bal,
between Mun and the one who spoke a number of
languages.
6. Jones was to the right of the rock collector and
opposite the pilot who was next to Rider.
Who was Aken’s friend?Submit Solution 4181 views
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Kim Jones, Jan Robinson and Pat Smith are the officers
of the spaceship. They serve as the craft’s pilot,
engineer and biochemist, though not necessarily in that
order. Because they have difficulty with Martian names,
they nickname the three Martians who work with them
Jones, Smith and Robinson.
1. Robinson is a Yomi.
2. Jones doesn’t speak any language other than
Martian.
3. Most Martian linguists are Uti.
4. The Martian who serves as interpreter respects the
Martian whose name is the same as the biochemist’s.
5. The Martian whose name is the same as the biochemist
is a Grundi.
6. Jan Robinson beat the engineer at chess.
Who is the pilot?Submit Solution 3536 views
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Martians don’t need to develop airplanes as a means
of moving through the air. Most feathered Martians can
fly easily. Every few lunars, feathered Martians from
the various groups participate in a tournament to determine
which are the best fliers of the planet.
This lunar, teams of two feathered Martians from
three groups are competing:
1. One team is from the Uti, one from the Grundi,
and one from the Yomi.
2. Each team is made up of one female and one male.
3. The female participants are Xera, Wora, and Teta.
4. The males are called Vel, Pyi, and Rir.
5. Despite her daring feats in the air, Teta had never
been away from home before the contest.
6. Xera and Rir had never met before the tournament.
7. Xera will be visiting Pyi’s group when the Yomi go
on a special excursion to that part of the planet.
8. Pyi admires Teta’s colorful feathers, as well as her
ability to soar, and once watched her and her teammate
in the territory of the Grundi.
If the winners are members of the Uti group, what
are the names of the best fliers?View SolutionSubmit Solution 3733 views
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You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighing, how do you find the defective one?
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You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.
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Three ants are sitting at the three corners of an equilateral triangle. Each ant starts randomly picks a direction and starts to move along the edge of the triangle. What is the probability that none of the ants collide?
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