A couple of interesting problems that require little or no formal training in Mathematics. These are the sought of questions you may be asked at the interview stage of your university application where candidates will be at different stages of different syllabuses and the interviewer wants to know what level of analytical reasoning the candidate is capable of.

1. How many edges does a 4-dimensional cube have?

HINT: Think of the pattern as you move up from 0 to 1 to 2...dimensions and you should be able to extrapolate the answer from what you know about the number of edges of cubes of 3 or less dimensions. Note: a 0/1/2 dimensional cube is a single vertex/line/square.

ANSWER: At bottom of page.

2. How many points on the globe are there where if you travel a mile North then a mile East and then a mile South you finish in the same place you started?

ANSWER: (Infinity squared) + 1: can be explained during tuition.

3. You have two regular polygons, one with Y sides and one with X sides (Y>X). Just as the polygon with Y sides has Y-X more sides than the polygon with X sides, each internal angle of the Y-sided polygon is Y-X degrees greater than each internal angle of the X-sided polygon. Y+X is a perfect square. What are the values of X and Y?

ANSWER: 40 and 9. Working can be explained during tuition.

4. Why are manhole covers round? This is more a lateral thinking than a mathematical problem.

ANSWER: Can be explained during tuition.

5. You have 8 billiard balls. One is heavier than the other seven that are all identicle in weight. You also have an old-fashioned set of scales and are allowed to use it for two weigh-ins. How can you know with these two weigh-ins which is the heavier billiard ball?

ANSWER: Can be explained during tuition - there is a way you can be 100% sure which one it is!

6. You have 6 sticks of equal length and need to make 4 equilateral triangles using the sticks. How can this be done?

ANSWER: Can be explained during tuition. 

ANSWERS

1. Although we have no conception of a fourth dimension existing in space we can give a precise answer.

A 0-dimensional cube is simply a single vertex.

A 1-dimensional cube is an edge. It is two vertices (0-dimensional cubes) with an edge joining the 'new' vertex to the 'old' vertex.

A 2-dimensional cube is a square. It is two edges (1-dimensional cubes) with edges connecting each of the 'new' vertices to one vertex on the 'old' edge.   

A 3-dimensional cube is a cube! It is two squares (2-dimensional cubes) with edges connecting each vertex in the 'new' square with one vertex in the 'old' square.

Extrapolating this pattern to the 4-dimensional case the cube will be two 3-dimensional cubes (2*12 edges) with edges connecting each of the 'new' vertices (of which there will be 8) to a corresponding 'old' vertice. Therefore the total number of edges in a 4-dimensional cube is 32.