Thursday, October 7, 2010
The Trader's Puzzle - Balance Weights
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Basic Algebra,
Loyd,
Puzzles
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About Me
- Curmudgeon
- I'm a high-school math teacher completely frustrated with new math, reform math, fuzzy math, the color of math, talking about math, literacy across the curriculum and all those other things that get in the way of students actually learning math, not to mention the ever-present "You need to help raise our scores by taking one day a week to go over test-taking skills" and other administrative folderol. (He/Him/Mr.)
Do you read Tanya Khovanova's blog? She posts lots of weighing puzzles. I think she did this one in the Spring.
ReplyDeleteHers went up to 40 grams (whole number increments). I like the answers here better, just going to 10 pounds.
http://blog.tanyakhovanova.com
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.
ReplyDeleteThat, and "lucky threes" should be a pretty good hint as to how the weights of the rings are chosen.