Being resilient

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Explore the effect of combining enlargements.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.