Small and Beautiful - September 2003, Stage 2&3

Problems

problem icon

A Conversation Piece

Stage: 2 Challenge Level: Challenge Level:1

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

problem icon

Which Is Quicker?

Stage: 2 Challenge Level: Challenge Level:1

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

problem icon

Folding, Cutting and Punching

Stage: 2 Challenge Level: Challenge Level:1

Exploring and predicting folding, cutting and punching holes and making spirals.

problem icon

Shapely Tiling

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

problem icon

1, 2, 3, 4, 5

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

problem icon

Sept03 Sept03 Sept03

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This number has 903 digits. What is the sum of all 903 digits?

problem icon

Folding

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What shapes can you make by folding an A4 piece of paper?

problem icon

Smaller and Smaller

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

problem icon

Fitted

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

problem icon

LOGO Challenge - the Humble Square

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

problem icon

Sept 03

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the last digit of the number 1 / 5^903 ?

problem icon

Repetitiously

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

problem icon

Hidden Squares

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

problem icon

Adding Triangles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the total area of the first two triangles as a fraction of the original A4 rectangle? What is the total area of the first three triangles as a fraction of the original A4 rectangle? If. . . .

problem icon

Terminology

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Triangle ABC is isosceles while triangle DEF is equilateral. Find one angle in terms of the other two.

problem icon

Rati-o

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

problem icon

Three Times Seven

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

problem icon

Six Times Five

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many six digit numbers are there which DO NOT contain a 5?

problem icon

Excel Investigation: Power Crazy

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

When is 7^n + 3^n a multiple of 10? Use Excel to investigate, and try to explain what you find out.