You may also like
Plutarch's Boxes
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
The Genie in the Jar
This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?
Age 11 to 14
Challenge Level
Why do this problem?
This problem gives practice in working with volume. It can be done by either trial and improvement or by using spreadsheets. It is a very good opportunity to see the value of using spreadsheets in solving problems.
Before tackling the problem, it might be valuable to investigate how the area of a rectangle can be maximised for a given perimeter.
Possible approach
Key questions
Possible support
Suggest trying Oh! Harry! which is a Stage 2 problem involving volume.
Possible extension
Learners could try Zin Obelisk, which is a similar problem.
NRICH is part of the family of activities in the Millennium Mathematics Project.