6 Sep 2013

Prize Maths Quiz: A Four-Pan Balance Puzzle (PMQ35)

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?

IMPORTANT CHANGES TO THE PRIZE MATHS QUIZ!

YOU MAY NOW DISCUSS THIS PMQ PROBLEM IN THE COMMENTS BELOW AND GIVE YOUR ANSWERS AND SOLUTION METHOD.

I HOPE THIS WILL MAKE THE COMMENTS MORE VIBRANT!

If you would like to DONATE PRIZES for the next PMQ, send me a message here.

How to Enter

IF YOU ARE A STUDENT, you may still send your complete solution by email to pmq33bernoulli@giftedmaths.comThis 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.
Anybody can enter our Prize Maths Quiz; adults and students.
Use the official server clock in the right column to avoid late entries.
All emails and email addresses sent to us will be deleted after the winners have been processed.
DO NOT submit your entries to the comments section at the bottom of this post.
You CAN discuss it there but you must email us to enter the competition.
We adhere to COPPA guidelines regarding children's online safety and security.
Enjoy the challenge!
Send us your solution! You can't win if you don't participate.