Thursday, October 7, 2010

The Trader's Puzzle - Balance Weights

What are the weights of the four rings to as to measure any desired weight from a quarter-pound up to ten, in quarter-pound increments?


  1. Do you read Tanya Khovanova's blog? She posts lots of weighing puzzles. I think she did this one in the Spring.

    Hers went up to 40 grams (whole number increments). I like the answers here better, just going to 10 pounds.

  2. There are three "states": left side, right side, unused. Therefore, there are 3*3*3*3 possible arrangements of the rings. Of these, one is "no rings" and the others can be logically reasoned to be symmetrical - for each arrangement there must be a mirror image. This means that the 81 possibilities are really 1 NULL, and 40 possible totals. This is where the "10 pounds in 1/4 pound increments" or the "40 pounds in 1 pound increments" comes from.

    That, and "lucky threes" should be a pretty good hint as to how the weights of the rings are chosen.