Brainteasers

23rd January 2004 at 00:00
Saturday job

Age 8-12

Kevin earns pound;10 a week for a Saturday job. He saves all that he earns.

Every so often, he takes the week off and spends pound;60 of his savings.

Last year he saved pound;100 overall from his Saturday job.

How many weeks did Kevin take off?

All tied up

Age 13-16

A cuboid parcel is to be secured with a piece of sticky tape 360cm in length.

The tape has to pass twice round the width of the parcel and once round the length.

There are no overlaps in the sticky tape.

What should be the length, width and height of the parcel to give it the maximum volume?

Brainteaser solutions from page 30 Saturday jobSavings of pound;100 overall are equivalent to 10 weeks of earnings. In the other 42 weeks of the year, or 6 lots of 7 weeks, Kevin saved nothing overall. So Kevin had 6 weeks off from his Saturday job.

All tied up A parcel 60cm x 30cm x 20cm has the maximum volume of 36,000 cubic centimetres.

The simplest way to think of the solution is to consider how to achieve the maximum volume by having the maximum length multiplied by the maximum width by the maximum height. The 360cm tape has to cover a = 2 x length, b = 4 x width and c = 6 x height The volume is proportional to the product abc, and is maximised when these three quantities take equal lengths of tape, ie 120cm. So: length = 120 V 2 = 60cm width = 120 V 4 = 30cm height = 120 V 6 = 20cm A graphical solution will lead to an answer.

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