Math are full of paradoxes. Many of them are simple and interesting for all of us. This is a collection of simple math and logical paradoxes from website aplusclick.com

1. Famous Math & Logic Paradoxes
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2. Bermuda Triangle
Why the sum of the interior angles of the Bermuda triangle is
not 180o?
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3. Barber Paradox
In a city, the barber is the 'one who shaves all those, and
those only, who do not shave themselves.’
Who shaves the barber?
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4. Achilles and the Tortoise
The great hero Achilles challenges a tortoise to a footrace. He agrees to
give the tortoise a head start of 100m. When the race begins, Achilles
starts running, so that by the time he has reached the 100m mark, the
tortoise has only walked 10m. But by the time Achilles has reached the
110m mark, the tortoise has walked another 1m. By the time he has
reached the 111m mark, the tortoise has walked another 0.1m, then
0.01m, then 0.001m, and so on. The tortoise always moves forwards
while Achilles always plays catch up. Why is Achilles always behind the
tortoise?
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5. Simpson Paradox
The average score for dance of boys and girls in class A are 16
and 21, respectively. The average score of boys and girls in class
B are 15 and 20, respectively. Twenty percent of class A students
are girls. Forty percent of class B students are girls. Which class
has a higher average score?
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6. Braess Paradox
The diagram shows a road network. All cars drive in one direction
from A to F. The numbers represent the maximum flow rate in
vehicles per hour. Engineers want to construct a new road with a
flow rate of 100 vehicles per hour. Drivers randomly choose the
road at crossroads. What new road decreases the capacity of
the network (the number of vehicles at point F)?
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7. Leonard Euler’s Paradox
Why the average of all of the numbers is not a zero?
1, -1, 2, -2, 3, -3, . . .
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8. Friendship Paradox
Your friends have more friends than you. Why?
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9. Uninteresting Number Paradox
How many uninteresting numbers are there?
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10. Gabriel’ Horn Paradox
The shape obtained from rotating the equation about x-axis
resembles a trumpet. If we need an infinite volume of paint to
paint the infinite horn, how much paint does the horn can contain
inside itself?
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11. Pop Quiz Paradox
A teacher announces that there will be a quiz one day during the
next week. The teacher gives the definition that they would not
when they come in to the class that the quiz was going to be
given that day. The brightest student says that the quiz cannot be
on Friday because they will know the day. With the same
technique, she eliminates Thursday, Wednesday, Tuesday, and
Monday. “You cannot give us a pop quiz next week” she says.
When does the teacher give the pop quiz? I know the paradox
from Charles Carter Wald. Probably, Martin Gardner described it
for the first time in The Colossal Book of Mathematics.
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12. Answers at
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