Conjecturing and generalising
-
-
problemFavouriteHow Many Miles to Go?
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
-
problemFavouriteCubes Within Cubes Revisited
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
-
problemFavouriteLitov's Mean Value Theorem
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
-
-
problemFavouriteCunning Card Trick
Delight your friends with this cunning trick! Can you explain how it works?
-
problemFavouriteConsecutive Negative Numbers
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
-
problemFavouriteSquare It
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
-
problemFavouriteArithmagons
Can you find the values at the vertices when you know the values on the edges?
-
problemFavouriteCyclic Quadrilaterals
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?