Working systematically

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Zias have 3 legs and Zepts have 7 legs. If there were 52 legs, how many of each were there?

Abundant numbers are less than the sum of their factors (excluding themselves). Can you find some?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Amy's mum gave her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you replace the letters with numbers? Is there only one solution in each case?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?