Weekly quiz          

2003/04

Qualifying round 1

Problems

Problem 1

That's odd

Hans had forgotten the pin code on his credit card.

He remembered that the pin code had four digits, and that it was an odd number.

He also remembered that the four digits were 0, 5, 6 and 7, and that the pin code did not start with 0.

How many possible pin codes could match his description?  

Problem 2

What is the length of the track?

The figure shows a track of a special shape.

CFG is an equilateral triangle. At the center of CG and CF we have drawn a square with sides equal to one third of the sides of the triangle.

The track is composed by four circular arches: One with its center in H, one with its center in I and two with their centers in C. The arch from A to B measures 90 meters. 

What is the length of the track?

Problem 3

Coin Combination

Eric, Jenny, Rebecca and Mitch each had $1.00 in coins.

- No one had pennies
- Each person had at least one quarter.
- Each person had a different number of quarters.
- Mitch had 1 more than 5 times as many nickels as Rebecca. 
- Rebecca had twice as many dimes as Eric.  
- Eric had fewer nickels than Rebecca.

For international students:
1 penny = 1 cent
1 nickel = 5 cents
1 dime = 10 cents
1 quarter = 25 cents
1 dollar ($1.00) = 100 cents

How many coins did they have all together?

Problem 4

The party problem

1/3 of the guests were women and one fourth were young girls. One sixth was men and there were six young boys. How many guests were at the party?

Write your answer in the box:

Problem 5

Beate's beads

Beate wants to follow the pattern above to make a necklace. She has plenty of red and blue beads to use, but only 10 white beads. She wants the necklace to be as long as possible.

The pattern does not have to fit when the ends are linked together.

When she finishes using her 10 white beads, how many red and blue beads will she have used?

a)  10

b)   20

c)  302

d)   50

e)   55

f)  65

Problem 6

Pizza discount

The 25cm (diameter) pizza sells for 50 kr at my favorite pizza store. The store claims they have a great deal on the large 30 cm pizza, which is specially priced at 58.50 kr. What is the per cent discount the store is offering, when we compare prizes according to how much pizza you get?

Round off your answer to the closest whole number:

Problem 7

Triangles in the pentagram

How many triangles can you find in the figure?

Write the number in the box:

Problem 8

Archimedes' mobile

a)  6

b)  18

c)  34

d)  123

e)  164

f)  288