WEEKLY QUIZ          

2004/05

Nordic final

Problems

1  Pentominoes in 3-D

Each shape consists of five basic cubes (here seen from above).

Your team is supposed to put together a symmetrical shape (Make it symmetrical around a plane).

The more cubes you use, the better.

2   Number Pyramid

On each lateral surface of the pyramid; place a flag with a number equal to the sum of the “corner numbers” of that surface. Ignore the vertex.

The number on the vertex equals the sum of the numbers on the lateral surfaces.

The number on the vertex is 20.

Place the other six numbers so that

a)     All numbers on the pyramid are different
b)     The same number may appear more than once.

3    Bird-tetrahedron

The bird-tetrahedron may be cut in two identical halves by a plane. The shape of the cross section in this plane is an equilateral triangle where the side equals s.

A) Explain the shape of the bird-tetrahedron.

B) Find an expression for the surface area of the bird-tetrahedron, based on s.

4   Guess the numbers!

Student A says: ”I don’t know your number”
Student B says: ”And I don’t know yours either”
Student A says: ”But then I know both our numbers!”

Find all possible number pairs and explain your reasoning. (There are four possible solutions.)

5  Afraid of the dark

You get four chips, labelled D (dad), M (mom), B (boy) and G (girl).

A family of four has to pass a dark tunnel. All of them are afraid of the dark. Fortunately they have a flashlight. The only problem is that the batteries will last for only 12 more minutes!

At most two people can pass the tunnel at any given time, and they have to walk at the speed of the slower of the two.

Dad is able to pass the tunnel in 1 minute, mom in 2 minutes, the boy in 4, and the girl in 5 minutes.

Will they make it?  If so, how?

19.05.05