You may also like
Trice
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Nine Colours
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Marbles in a Box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Age 11 to 14 Short
Challenge Level
The 4, 5 and 6 will be involved in the largest possible products, so we can begin by seeing whether they touch.
The 4 and the 5 do not touch, as shown in the diagram below, which shows part of the folded net.
The 4 and the 5 do not touch, as shown in the diagram below, which shows part of the folded net.
The 6 touches the 4 and the 5, as shown.
This means that the greatest product must include the 6 and the 5 or the 6 and the 4.
Clearly it will include the 3, not the 1, and so it will be 6$\times$5$\times$3 = 90.
Clearly it will include the 3, not the 1, and so it will be 6$\times$5$\times$3 = 90.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
Copyright © 1997 - 2021. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.