You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.

You have a dozen (12) stones weighing a whole number of grams between 1 and 6 each. You can obtain one reference weight of your choosing.

What reference weight can you choose to be able to figure out the individual weights of the 12 stones using a balance device for any possibility that may exist therein?

For an encore: what is the maximum weight range of stones (1 to N) that you could solve using 2 reference weights of your choice? Provided you can have as many stones as you need.

I don't believe, I have solved this one myself. We could make it a community project after the first question is answered.

HISTORICAL NOTE:

This problem originated on Brain Den. I constructed it based on Bonanova's problem Weighty Thoughts: http://brainden.com/forum/index.php/topic/4932--/?p=84107 few years ago.

Back then limited number of people participated. The solution found was for specific numbers in that problem (range 1 to 5) – not general. I'd like to give it another try.

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