# User:Miss Puzzle/sandbox

Page 1:

Boy and Girl

A boy and a girl are talking.

"I am a boy" - said the child with black hair.
"I am a girl" - said the child with white hair.

At least one of them lied. Who is the boy and who is the girl?

If only one of them had lied, we'd have to conclude that both are boy or both are girl. This is impossible, so both of them must have lied. Therefore, the child with the black hair is the girl, and the child with the white hair is the boy. If only one of them had lied, we'd have to conclude that both are boy or both are girl. This is impossible, so both of them must have lied. Therefore, the child with the black hair is the girl, and the child with the white hair is the boy.

--- Page 2:

2 Million Currencies

What sentence about an integer ${\displaystyle \,n}$ is true if, and only if the values ${\displaystyle \,n}$ takes are less than two million?

n is an integer that is less than 2000000.

n is an integer that is either negative, 0, has fewer than 7 digits, or has 7 digits and its first digit is 1.

n/2 < 1 000 000 |n being an integer

--- Page 3:

Boy, girl and dog

A boy, a girl, and a dog simultaneously begin their movement from one point. The boy and girl are heading in one direction, with speed 5 km/h for former and 4 km/h for latter. The dog runs from boy to girl and back with speed 10 km/h. Given that it takes no time for the dog to change direction, how much will the dog travel in 1 hour?

Since the dog travels at 10 km/hr, in 1 hour it will cover 10 km.

The boy moves at 5km/hr the girl at 4km/hr. The distance between the boy and girl will increase linearly over the one hour, up to its maximum of 1km. During this time the dog has been running back and forth at 10km/hr.

The boy moves at 5km/hr the girl at 4km/hr, but we don´t know for how long they have being moving. They could have just started to move and there´s virtually no distance between them. So the dog, whatever his speed, could just had travel a couple meters.

--- Page 4:

1 , 2 and 3

Put a mathematical character between "2" and "3" to get a number that is more than two and less than three. NOTE: You can't change the number sequence, therefore ${\displaystyle {\frac {3}{2}}}$ is not a correct answer (It is less than 2)

2.3

2 ${\displaystyle \ln }$ 3

--- Remove

Solution ---