Working systematically

There is a particular value of x, and a value of y to go with it, which make all these five expressions equal in value. Can you find that x, y pair?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

Can you match up these equivalent algebraic expressions?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Can you work out the probability of winning the Mathsland National Lottery?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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