Weekly quiz          

2003/04

Nordic final

Problems

1  "Olympic - like" rings

 
You are given 5 circles that overlap almost like the Olympic rings.  

This results in 9 areas.

The numbers from 1-9 should be placed in the areas, one number in each, such that numbers in each circle add up to the same sum.

Find the sum and put the numbers in the right place.

2  Dissection of squares

a)Cut a square into three congruent parts

      b)Cut a square into three similar parts, just two of which are congruent. (You can find more than one solution)

3   Longest routes

Set of conditions

A:   Every pin is visited once and once only

B:   There are no crossings

Find the longest route on the 9-pin board

4   Wheel combinations

Bill´s Bike Store sells bicycles, tricycles and wagons. Bill was a former math teacher and he decides to give his customers a problem to solve. He tells them:

In my workroom I have a combination of bicycles, tricycles and wagons that holds 17 wheels all together.

If you can tell me all possible combinations of vehicles that might be in my workroom, I will give you a 20% discount on anything you buy in my store.

Can you solve the problem? I might not have all three items in my workroom.

a) How can you know that you have all combinations?

b) Give some characteristics of the possible combinations.

5   Cubes combination

You are given a number of cubes that can be build together.

Construct the following:

All unique arrangements of four or fewer cubes, where unique means that it must differ from other arrangements even when rotated and/or flipped.

Extra problem

Arrange 9 playing cards like this (as seen above).

All rows and columns have a sum of 6, as well as one main diagonal, but the other diagonal has a sum of 3.

Change the positions of three cards to make the square completely magic (all rows, columns and both diagonals have the same sum).