MATH 190 Study Guide - Final Guide: Weighing Scale, Old Chinese, Roman Numerals

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 190
• Professor: Malgorzata Dubiel

Document Summary

Part i: you have a pan balance and ve weights weighing 1g, 2g, 4g, 8g and 16g respectively. Show how you can use these weights (putting them only on one side of the balance) to weigh any object whose weight is an exact number of grams between 1g and 31g. Every positive integer can be expressed in binary notation. 10111 in binary which means that 23 is equal to 24 + 22 + 21 + 20. In terms of the balance 23 grams can be weighed by placing the 16, 4, 2, 1 gram weights in the other pan. In other words, every integer can be written as a sum of powers of 2 with no power being repeated. Integers up to 31 need only powers of 2 up to 24 = 16 because 25 = 32. Below is a table showing the combinations for all integer gram weights from 2 to 31 grams. integer combination integer combination integer combination.