There is a new kind of balance scale that has three weighing pans. When you put things in the pans, the pans will indicate the relative heaviness of each thing or group of things being weighed. For example, if something in pan one weighed 3, and the thing in pan two weighed 4 and the thing in pan three weighed 5, pan three would hang lower than pan two which would hang lower than pan one. Likewise, if you weighed things that were 4, 4 and 2, the pan with the 2 in it would hang higher than the other two pans, which would hang at the same height.
There are a group of marbles that all look exactly alike. Genuine marbles weigh 10. But, you know there is a counterfeit marble that weighs 9 and another counterfeit marble that weighs 11. If you can only use the scale twice, what is the maximum number of marbles you can have, where you would be guaranteed to identify the light and heavy marble?
Question
Guest
There is a new kind of balance scale that has three weighing pans. When you put things in the pans, the pans will indicate the relative heaviness of each thing or group of things being weighed. For example, if something in pan one weighed 3, and the thing in pan two weighed 4 and the thing in pan three weighed 5, pan three would hang lower than pan two which would hang lower than pan one. Likewise, if you weighed things that were 4, 4 and 2, the pan with the 2 in it would hang higher than the other two pans, which would hang at the same height.
There are a group of marbles that all look exactly alike. Genuine marbles weigh 10. But, you know there is a counterfeit marble that weighs 9 and another counterfeit marble that weighs 11. If you can only use the scale twice, what is the maximum number of marbles you can have, where you would be guaranteed to identify the light and heavy marble?
Link to comment
Share on other sites
21 answers to this question
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.