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?

a)    2

b)    8

c)    10

d)    18

e)    24

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?

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?

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:

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?

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:

a)    3%

b)    17%

c)    19%

d)    20%

e)    23%

Triangles in the pentagram

How many triangles can you find in the figure?

Write the number in the box:

Archimedes' mobile

Archimedes did several discoveries on balance and equilibrium.

The discoveries may be used on mobiles.

What is the sum of the weights of the three red balls?

(You should not take into account the weight of the string and the little sticks, only the balls.)

Cross out your answer:

Problem 1

That's odd

There are 8 possible pin codes:
6507
5607
6057
5067
6705
7605
6075
7065

Problem 2

What is the length of the track?

There are two semi circles with centers H and I. These are all together 360 m. The arch BD is one sixth of a circle with the same radius as the semi circles, which gives 60 m. The arch GF is one sixth of a circle with three times the radius and the other circles, which gives 180 m.

The whole track has the length 360m + 60m + 180m = 600m

Problem 3

Coin Combination

                        Quarters           dimes               nickels
Mitch                1                      2                      11
Rebecca           2                      4                      2
Eric                  3                      2                      1
Jenny               4                      0                      0

They had 32 coins all together.  

Problem 4

The party problem

The six young boys were 1 – 1/3 – ¼ - 1/6 = ¼ of the guests. Then it is 6x4=24 guests.  

Problem 5

Beate´s beads

She will have used 55 blue and red beads. The pattern unit is:

R-H-R-R-B-B

That means she uses three red and two blue beads for each white. In ten pattern units she uses 50 red and blue beads. On each side she can add beads as shown:

R-R-B-B- XXXXXXXXXXXX-R

That is 50 + 5 = 55 blue and red beads all together.

Problem 6  

Pizza discount

The large pizza costs: 58.50 kr : (π ∙ 15² cm²) = 0.0828 kr/cm²

The small pizza costs: 50 kr : (π ∙ 12.5² cm²) = 0.1019 kr/cm²

The discount in per cent is:

( (0.1019 kr/cm² – 0.0828 kr/cm² ) ∙ 100% ) : 0.1019 kr/cm²   = 18.8% ≈ 19%

Problem 7

Triangles in the pentagram

35 triangles all together

5 of each triangle give 4 x 5 = 20 triangles

  5 of each of these give 2 x 5 = 10 triangles

  and finally 5 triangles  

Problem 8

Archimedes’ mobile

Counting upwards, using the balance principle, one gets that the red ball to the right weighs 128. All the balls at the right side of the whole mobile are then 256. Naming the bottom red ball x, we get that the upper left red ball weighs 8x, and the whole left side and the mobile weighs 64x. This equals the right side, which is 256.

Hence x=4, and the total of the red balls are 4 + 32 + 128 = 164