# October 2002, All Stages

## Problems

### Making Sticks

##### Stage: 1 Challenge Level:

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

### Grouping Goodies

##### Stage: 1 Challenge Level:

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

### Multiplication Squares

##### Stage: 2 Challenge Level:

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

### A Right Charlie

##### Stage: 2 Challenge Level:

Can you use this information to work out Charlie's house number?

### Scoring with Dice

##### Stage: 2 Challenge Level:

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

### Divide it Out

##### Stage: 2 Challenge Level:

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

### Factor Lines

##### Stage: 2 and 3 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

### LOGO Challenge 8 - Rhombi

##### Stage: 2, 3 and 4 Challenge Level:

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

### Remainder

##### Stage: 3 Challenge Level:

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

### Oh for the Mathematics of Yesteryear

##### Stage: 3 Challenge Level:

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

### X Marks the Spot

##### Stage: 3 Challenge Level:

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

### Excel Technique: Inserting an Increment Button

##### Stage: 3 and 4 Challenge Level:

Learn how to use increment buttons and scroll bars to create interactive Excel resources.

### Excel Technique: Making a Table for a Function of Two Independent

##### Stage: 3 and 4 Challenge Level:

Learn how to make a simple table using Excel.

### Excel Interactive Resource: Make a Copy

##### Stage: 3 and 4 Challenge Level:

Investigate factors and multiples using this interactive Excel spreadsheet. Use the increment buttons for experimentation and feedback.

### Excel Investigation: Ring on a String

##### Stage: 3 and 4 Challenge Level:

This investigation uses Excel to optimise a characteristic of interest.

##### Stage: 3 and 4 Challenge Level:

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

### Number Rules - OK

##### Stage: 4 Challenge Level:

Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...

### Back to Basics

##### Stage: 4 Challenge Level:

Find b where 3723(base 10) = 123(base b).

### Diagonals for Area

##### Stage: 4 Challenge Level:

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

##### Stage: 5 Challenge Level:

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

### Diverging

##### Stage: 5 Challenge Level:

Show that for natural numbers x and y if x/y > 1 then x/y>(x+1)/(y+1}>1. Hence prove that the product for i=1 to n of [(2i)/(2i-1)] tends to infinity as n tends to infinity.

### Sine Problem

##### Stage: 5 Challenge Level:

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.