Being curious

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

If you move the tiles around, can you make squares with different coloured edges?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Here are shadows of some 3D shapes. What shapes could have made them?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?