Working systematically

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

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?

This dice train has been made using specific rules. How many different trains can you make?

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