Red faces

A cube made of white plastic is painted red on the outside. It is then cut into smaller cubes as shown in the diagram.

a What is the least number of cuts needed to make the smaller cubes?

b How many smaller cubes are produced?

c How many red faces will the smaller cubes have altogether?

d How many white faces will there be?

SOLUTIONS Red faces age 7 to 11, a 6 cuts, b 27 smaller cubes, c 54 red faces, d 108 white faces. There are 9 x 6 = 54 red faces of smaller cubes on the 6 faces of the 3 by 3 by 3 cube. The 27 smaller cubes have a total of 27 x 6 = 162 faces, so 162 - 54 = 102 must be white.

Multiplication

Each * stands for a missing digit.

4** x 3** = ***500

3***0 x 8**= ***3**

What is the answer to this problem

SOLUTIONS Multiplication age 10 to 14. The units digit of the first number must be 5 and of the second number must be 2. The middle digit of the first number must be 1, 2, 3 or 4, and of the second number must be 8 or 9.

Trying the possibilities systematically provides the answer.