Weekly Problem 27 - 2007

Ten stones form an arch. What is the size of the smallest angles of the trapezoidal stones?

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

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

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

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

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

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

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

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

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

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

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

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

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

Which countries have the most naturally athletic populations?

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