Being resilient

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?

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?

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?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

How many different triangles can you make on a circular pegboard that has nine pegs?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Will you play the nice or the nasty version of this dice game?