Here are three answers:
Answer A Answer A or B Answer B or C There is only one correct answer to this
question. Which answer is this?
If answer A would be correct, then answer B ("Answer A or B") would also be
correct. If answer B would be correct, then answer C ("Answer B or C") would
also be correct. This leads to the conclusion that if either answer A or answer
B would be the correct answer, there are at least two correct answers. This
contradicts with the statement that "there is only one correct answer to this
question". If answer C would be correct, then there are no contradictions. So
the solution is: answer C.
Hans is standing behind
Gerrie and at the same time Gerrie is standing behind Hans. How is this possible
Hans and Gerrie are standing with their backs towards each other!
A cyclist drove one
kilometer, with the wind in his back, in three minutes and drove the same way
back, against the wind in four minutes. If we assume that the cyclist always
puts constant force on the pedals, how much time would it take him to drive one
kilometer without wind?
The cyclist drives one kilometer in three minutes with the wind in his back, so
in four minutes he drives 1 1/3 kilometer. Against the wind, he drives 1
kilometer in four minutes. If the wind helps the cyclist during four minutes and
hinders the cyclist during another four minutes, then - in these eight minutes -
the cyclist drives 2 1/3 kilometers. Without wind, he would also drive 2 1/3
kilometers in eight minutes and his average speed would then be 17.5 kilometers
per hour. So it will take him 3 3/7 minutes to drive one kilometer.
Three salesmen went into a
hotel to rent a room. The manager stated that he had only one room left, but all
three could use it for $30.00 for the night. The three salesmen gave him $10.00
each and went up to their room. Later, the manager decided that he had charged
the salesmen too much so he called the bellhop over, gave him five one-dollar
bills, and said: 'Take this $5.00 up to the salesmen and tell them I had charged
them too much for the room'. On the way up, the bellhop knew that he could not
divide the five one-dollar bills equally so he put two of the one-dollar bills
in his pocket and returned one one-dollar bill to each of the salesmen. This
means that each salesman paid $9.00 for the room. The bellhop kept $2.00. Three
times nine is 27 plus two is 29....... What happened to the extra dollar?
The calculation just makes no sense. The three salesman paid $27, of which the
manager got $25 and the bellhop $2. Conclusion: There's no dollar missing at
all.
A cyclist drove one
kilometer, with the wind in his back, in three minutes and drove the same way
back, against the wind in four minutes. If we assume that the cyclist always
puts constant force on the pedals, how much time would it take him to drive one
kilometer without wind?
The cyclist drives one kilometer in three minutes with the wind in his back, so
in four minutes he drives 1 1/3 kilometer. Against the wind, he drives 1
kilometer in four minutes. If the wind helps the cyclist during four minutes and
hinders the cyclist during another four minutes, then - in these eight minutes -
the cyclist drives 2 1/3 kilometers. Without wind, he would also drive 2 1/3
kilometers in eight minutes and his average speed would then be 17.5 kilometers
per hour. So it will take him 3 3/7 minutes to drive one kilometer.
Below is an equation that
isn't correct yet. By adding a number of plus signs and minus signs between the
ciphers on the left side (without changes the order of the ciphers), the
equation can be made correct. 123456789 = 100 How many different ways are there
to make the equation correct?
There are 11 different ways:
123+45-67+8-9=100
123+4-5+67-89=100
123-45-67+89=100
123-4-5-6-7+8-9=100
12+3+4+5-6-7+89=100
12+3-4+5+67+8+9=100
12-3-4+5-6+7+89=100
1+23-4+56+7+8+9=100
1+23-4+5+6+78-9=100
1+2+34-5+67-8+9=100
1+2+3-4+5+6+78+9=100
Remark: if it is not only allowed to put plus signs and minus signs between the
ciphers, but also in front of the first 1, then there is a twelfth possibility:
-1+2-3+4+5+6+78+9=100.
Tom has three boxes with
fruits in his barn: one box with apples, one box with pears, and one box with
both apples and pears. The boxes have labels that describe the contents, but
none of these labels is on the right box. How can Tom, by taking only one piece
of fruit from one box, determine what each of the boxes contains?
Tom takes a piece of fruit from the box with the labels 'Apples and Pears'. If
it is an apple, then the label 'Apples' belong to this box. The box that said
'Apples', then of course shouldn't be labeled 'Apples and Pears', because that
would mean that the box with 'Pears' would have been labeled correctly, and this
is contradictory to the fact that none of the labels was correct. On the box
with the label 'Appels' should be the label 'Pears'. If Tom would have taken a
pear, the reasoning would have been in a similar way.
Richard is a strange liar.
He lies on six days of the week, but on the seventh day he always tells the
truth. He made the following statements on three successive days: Day 1: "I lie
on Monday and Tuesday." Day 2: "Today, it's Thursday, Saturday, or Sunday." Day
3: "I lie on Wednesday and Friday." On which day does Richard tell the truth?
We know that Richard tells the truth on only a single day of the week. If the
statement on day 1 is untrue, this means that he tells the truth on Monday or
Tuesday. If the statement on day 3 is untrue, this means that he tells the truth
on Wednesday or Friday. Since Richard tells the truth on only one day, these
statements cannot both be untrue. So, exactly one of these statements must be
true, and the statement on day 2 must be untrue. Assume that the statement on
day 1 is true. Then the statement on day 3 must be untrue, from which follows
that Richard tells the truth on Wednesday or Friday. So, day 1 is a Wednesday or
a Friday. Therefore, day 2 is a Thursday or a Saturday. However, this would
imply that the statement on day 2 is true, which is impossible. From this we can
conclude that the statement on day 1 must be untrue. This means that Richard
told the truth on day 3 and that this day is a Monday or a Tuesday. So day 2 is
a Sunday or a Monday. Because the statement on day 2 must be untrue, we can
conclude that day 2 is a Monday. So day 3 is a Tuesday. Therefore, the day on
which Richard tells the truth is Tuesday.
Assume that you have a
number of long fuses, of which you only know that they burn for exactly one hour
after you lighted them at one end. However, you don't know whether theyburn with
constant speed, so the first half of the fuse can be burnt in only ten minutes
while the rest takes the other fifty minutes to burn completely. Also assume
that you have a lighter. How can you measure exactly three quarters of an hour
with these fuses? Hint: 2fuses are sufficient to measure three quarter of an
hour Hint: A fuse can be lighted from both ends at the same time(which reduces
its burning time significantly)
With only two fuses that burn exactly one hour, one can measure three quarters
of an hour accurately, by lighting the first fuse at both ends and the other
fuse at one end simultaneously. When the first fuse is burnt out after exactly
half an hour (!) you know that the second fuse still has exactly half an hour to
go before it will be burnt completely, but we won't wait for that. We will now
also light the other end of the second fuse. This means that the second fuse
will now be burnt completely after another quarter of an hour, which adds up to
exactly three quarters of an hour since we started lighting the first fuse!
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