Your Solutions - Stage 3 & 4

Trapezium Arch

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

Weekly Problem 27 - 2007
Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?

Common Remainder

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

144 divided by n leaves a remainder of 11. 220 divided by n also leaves a remainder of 11. What is n?

Red Card Blue Card

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

Can you arrange the red and blue cards so that the rules are all followed?

Equal Means

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

What value of x makes the mean of the first three numbers in this list equal to the mean of the other four?

Magic 7

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

Can you complete this magic square with the numbers from 7 to 15?

Counting Factors

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

Is there an efficient way to work out how many factors a large number has?

Latin Numbers

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

Can you create a Latin Square from multiples of a six digit number?

Calendar Capers

Stage: 3 Challenge Level: Challenge Level:1

Choose any three by three square of dates on a calendar page...

Rationals Between...

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you find between the square roots of 65 and 67?

Gift of Gems

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Four jewellers share their stock. Can you work out the relative values of their gems?

An Equilateral Triangular Problem

Stage: 3 Challenge Level: Challenge Level:1

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

Star Polygons

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

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Angles in Three Squares

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

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

Polygon Pictures

Stage: 3 Challenge Level: Challenge Level:1

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Who's the Best?

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

Which countries have the most naturally athletic populations?

Do Rare Events Happen?

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

I'd be very surprised if I had three children all with the same birthday, but I read in the paper that it happened to one family...

Gabriel's Problem

Stage: 3 Challenge Level: Challenge Level:1

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?