Hard Puzzles

The Paradox of Achilles and the Tortoise is one of a number of theoretical discussions of movement put forward by the Greek philosopher Zeno of Elea in the 5th century BC. It begins with the great hero Achilles challenging a tortoise to a footrace. To keep things fair, he agrees to give the tortoise a head start of, say, 500m. When the race begins, Achilles unsurprisingly starts running at a speed much faster than the tortoise, so that by the time he has reached the 500m mark, the tortoise has only walked 50m further than him. But by the time Achilles has reached the 550m mark, the tortoise has walked another 5m. And by the time he has reached the 555m mark, the tortoise has walked another 0.5m, then 0.25m, then 0.125m, and so on. This process continues again and again over an infinite series of smaller and smaller distances, with the tortoise always moving forwards while Achilles always plays catch up.
Logically, this seems to prove that Achilles can never overtake the tortoise—whenever he reaches somewhere the tortoise has been, he will always have some distance still left to go no matter how small it might be. Except, of course, we know intuitively that he can overtake the tortoise. The trick here is not to think of Zeno’s Achilles Paradox in terms of distances and races, but rather as an example of how any finite value can always be divided an infinite number of times, no matter how small its divisions might become.
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Below are thirteen 5 lettered, everyday words, each of which has had two of its letters removed.
In total these 26 letters are AZ. The remaining letters in each word are in the correct order.
There are no words which are spelled differently based upon location (favour/favor, etc) and there are no plurals.
Can you determine the original words?
APE
BAE
BOD
ANC
ROE
ELL
RAY
BUC
ORA
UMB
SUA
LOL
GESView SolutionSubmit Solution 3892 views
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Naga a safari in the kajiranga jungle capture three men. The naga give the men a single chance to escape uneaten.
The prisoner are lined up in order of height, and are tied to stakes. The man in the rear can see the backs of his two friends, the man in the middle can see the back of the man in front, and the man in front cannot see anyone. The Nagas show the men five hats. Three of the hats are black and two of the hats are white.
Blindfolds are then placed over each man’s eyes and a hat is placed on each man’s head. The two hats left over are hidden. The blindfolds are then removed and it is said to the men that if one of them can guess what color hat he is wearing they can all leave unharmed.
The man in the rear who can see both of his friends’ hats but not his own says, “I don’t know”. The middle man who can see the hat of the man in front, but not his own says, “I don’t know”. The front man who cannot see ANYBODY’S hat says “I know!”
How did he know the color of his hat and what color was it?
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There are two tribes in Mars, Lie tribe and Truth Tribe.
Lie tribe always speaks lie, True tribe always speaks truth.
You meet three mars people and ask
From First Person: What tribe you belong to?, he replies something in his language which you don’t understand.
Second person tells that he is saying that he belongs to Lie Tribe.
Third person says that second person is lying.
What tribe does the third person belong to?
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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 7550 views
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To enlist the help of the other kingdoms, the king talked to the queen about inviting neighboring royalty to dinner. This put the queen into a royal snit. Theirs was not a very wealthy kingdom and the royal dinnerware was in a disgraceful condition. Apart from ordinary dishes for everyday use, all that the royal pantry contained were a few dinner plates of three different
dinner patterns:
1. five silver ones with birds
2. six crystal with seashells
3. seven gold with the royal crest
They were all stored in disarray on a very dark top shelf of the royal pantry. Only those would be suitable for entertaining other royalty.
If the queen didn’t want to climb up to the top shelf twice, how many dinner plates would she have to take down to be sure she had matching dinner plates for herself, her royal spouse, and for the neighbouring king and queen?View SolutionSubmit Solution 5430 views
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Four Martians from different groups, the Uti,
Grundi, Yomi and Rafi, gathered for an intraplanetary
conference to discuss the problem of the visiting Earthlings.
As was appropriate for diplomatic envoys, all
were beautifully feathered in different colors, one red,
one green, one blue and the fourth brown. Their names
were Aken, Bal, Mun and Wora.
1. Before the meeting, the Uti had a pleasant breakfast
with Mun.
2. After debating with the Martians in the blue and
the brown feathers, Bal and the Yomi were so angry
that they tore a wingful of feathers out of them
before they were stopped.
3. Wora and the Rafi, however, agreed with the diplomat
with brown feathers, though they disagreed
with the redfeathered Grundi.
Who is the bluefeathered diplomat and to what
group does he or she belong?View SolutionSubmit Solution 3968 views
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There was trouble from the Grundi. One of them
damaged the spaceship by hurling a rock at it. The
astronauts couldn’t figure out what the Grundi had to
gain by their hostile act. Was it just vandalism, done out
of sheer spite? Or perhaps not everyone on Mars was
happy to see the Earthlings return.
The Martian police chief brought in five Grundi for
questioning. Like all Grundi, they sometimes told the
truth and sometimes lied. The suspects each made
three statements, two of which were true and one of
which was false. And the guilty one was revealed.
1. Zum said:
I am innocent.
I have never used a rock to destroy anything.
Tset did it.
2. Uk said:
I did not do the damage.
The Earthman’s vehicle is on Grundi space.
Yan is not my friend.
3. Pala said:
I am innocent.
I never saw Yan before.
Tset is guilty.
4. Tset said:
I did not throw the rock.
Yan did it.
Zum did not tell the truth when he said I did it.
5. Yan said:
I am innocent.
Uk is guilty.
Pala and I are old friends.
Who was the culprit?View SolutionSubmit Solution 4139 views
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