Some steps are built using 36 wooden blocks as shown in the diagram

All the faces on the outside except the bottom ones are painted blue. How many blocks do not get any of their faces painted ?

In the year 5 classroom, the desks are arranged in equal rows, Phil sits at the desk that is fourth from the front and third from the back. There are four desks on the right of Phil’s desk but only one to the left. How many desks are there in the room ?

A carpenter made 20 chairs and stools with a total number of 73 legs

If the chairs each have 4 legs and the stools each have 3 legs, how many chairs did she make ?

Lisa collected 50 seashells over a period of five days. Each day she collected three more than she had collected the day before. How many shells did she collect on the fifth day ?

An apartment block has a number of square apartments and a number of square gardens. Apartments must have at least one window, either to the out side or to a garden. In figure 1, one apartment has a window to an internal garden G, and ten have windows to the outside.

What is the smallest number of gardens needed for an apartment block built on a 6 x 6 square, as in figure 2, so that each apartment has a window to the outside or to an internal garden ?

Ace, Bea, Cec, Dee, Eve, Fie and Geo are 1, 2, 3, 4, 5, 6 and 7 years old, in some order. Dee is three times as old as Bea. Cec is four years older than Eve. Fie is older than Ace and Ace is older than Geo, but the combied ages of Ace and Geo is greater than the age of Fie. What is Ace’s age ?

In my marble bag there are between 40 and 80 marbles

If I share them equally among 4 children there is 1 left

If I share them equally among 5 children there is 3 left

If I share them equally among 6 children there is 1 left

How many marbles do I have ?

I am thinking of a number. It has three digits and is between 110 ans 140. The sum of the digits is 9 and the number is even. What is this number ?

Each of Andrew, Bill, Clair, Daniel and Eva either always lies or is always truthful, and they know who each of them is

Andrew says that Bill is a liar

Bill says that Clair is a liar

Clair says that Daniel is a liar

Daniel says that Eva is a liar

What is the largest possible number of liars in the group ?

When I opened my new maths book the sum of the two page numbers facing me was 317. What was the number of the next page ?

A rectangular wire grid is made up of 15 equal squares as shown. If the length of the grid is 20 cm, what is the total length, in centimetres, of the wire in the grid ?

A square piece of paper is folded along its centre lie and then folded again as shown

A cut is made along the dotted line in the third diagram. Which of the following could be the shape of the paper when it is unfolded ?

Two L shaped solids are each made up from 4 cubes as shown in the left of the diagram. The two shaded faces are glued together to form the solid shown on the right in the diagram.

How many faces of the original 8 cubes are visible if we can look at the solid from any angle ?

How many three-digit numbers greater than 900 are there that satisfy the following conditions ?

The sum of the digits is 14

The digits are all different

The tens digit is an odd number

Alice and Kate collect some seashells. Together they have 30 seashells. Which could NOT be true ?