Being resourceful

Want a serious challenge? Have a look at these ideas for changing the Approaching Midnight game.

How many were going to St Ives?

How can Agent X transmit data on a faulty line and be sure that her message will get through?

Can you tangle yourself up and reach any fraction?

Which of these logarithmic challenges can you solve?

Can you solve the system of equations to find the values of x, y and z?

Can you find the sum of the squared sine values?

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Can you hit the target functions using a set of input functions and a little calculus and algebra?

Can you use numerical methods to solve this equation to 1 decimal place?