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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.
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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.