An Invitation to Abstract Mathematics by Béla Bajnok

Author:Béla Bajnok
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

(b)How many measuring weights are needed if they can be placed on either pan?

(c)Suppose that you know that the item you need to measure has an integer weight somewhere between 1 and n units. What is the minimum number of measuring weights that you will need to have available so that you are guaranteed to be able to identify the weight of the item? (As in part (b), the weights can be placed on either pan.)

(Hint: Observe that for n = 3, a single measuring weight of 2 units suffices.)

7. Some Are Sums. (a)Let us say that a positive integer is accommodating if it can be written as the sum of (at least two) consecutive positive integers. For example, , , and are accommodating. Prove that a number is accommodating if, and only if, it is not a (nonnegative integer) power of 2.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.