Being resilient

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

How many symmetric designs can you make on this grid? Can you find them all?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Can you find all the different triangles on these peg boards, and find their angles?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Five children are taking part in a climbing competition with three parts, where their score for each part will be multiplied together. Can you see how the leaderboard will change depending on what happens in the final climb of the competition?