Yesterday, we looked at a problem involving a spice trader and his weights. Today, you are going to be the spice trader.
Imagine you have a four-pan balance, as illustrated below. The two outer pans are twice the distance from the fulcrum as the inner pans, the whole arrangement being balanced at the start.
You have a set of weights calibrated to be whole number ounces but you really don't want to carry them all with you. You wish to be able to weigh every amount between 0.5 to 32 ounces inclusive, going up in steps of 0.5 ounces, and to do so in one weighing.
What set of weights should you take, given that you want the smallest number of weights and the smallest sum of their weights?
Is your answer unique, or is there more than one solution?
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How to Enter
IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.com. This email address shall be removed after the competition closes to avoid spam. This PMQ35 competition closes on WEDNESDAY 11 SEPTEMBER at 23:59 GMT.
The Prize
The prizes for this PMQ are 3 free places in our Online Maths Club for ONE YEAR. The very first correct solution will receive a prize plus two others randomly selected from all the other correct answers. The email time stamp shall determine the order of entries received. All winners can have their name posted and a link to their own online profile at their favourite social network or their own blog.
Quick Rules
Look at the expanded rules on our PMQ page.
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Enjoy the challenge!
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