Being resilient

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Can you find ways to put numbers in the overlaps so the rings have equal totals?

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?