1 / 4

Weighing with a Balance

Weighing with a Balance. A large container is known to hold 24 oz of nails. The hardware store has a balance, but no weights. Can you measure out 9 oz of nails for a customer?.

grahams
Download Presentation

Weighing with a Balance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Weighing with a Balance A large container is known to hold 24 oz of nails. The hardware store has a balance, but no weights. Can you measure out 9 oz of nails for a customer? A chemist has a balance and fixed weights of 1, 2, 4, and 8 grams. Show that she can weigh any amount of material from 1 to 15 grams by placing the weights on one side and the material on the other. What is the best set of four fixed weights in the sense of maximizing the range of measurable weights in increments of 1 gram? Binary Search

  2. Find the Lighter Counterfeit Coin We have three coins. Two are normal coins; one is a counterfeit coin that weighs less. Identify the counterfeit coin with one weighing on a balance. We have nine coins; eight normal coins and a counterfeit coin that weighs less. Identify the counterfeit with 2 weighings. Generalize: How many weighing with a balance are needed to find a light counterfeit coin among n coins? How should we change the procedures above if the counterfeit coin is known to be heavier than normal ones? Binary Search

  3. 12 Coins with 1 Counterfeit: Lighter or Heavier We have 12 coins. Eleven are normal coins; one is a counterfeit coin that weighs less or more than a normal coin. Identify the counterfeit coin and its relative weight with a minimum number of weighings on a balance. Hint: First do it for 3 coins, one of which is a counterfeit, using only two weighing, Binary Search

  4. L L L np L L B 7– L L R L B L L B B L B R L R L L R B L R R B L L B L B B L R B B L B B B np B B R B R L B R B B R R R L L R L B R L R R B L R B B R B R R R L R R B 7+ R R R np Another Solution to the 12-Coin Puzzle We have 12 coins. Eleven are normal coins; one is a counterfeit coin 1 5 9 4 8 12 2 6 10 3 7 11 1 4 6 10 against 5 7 9 12 2 5 4 11 against 6 8 7 10 3 6 5 12 against 4 9 8 11 Each weighing has three possible outcomes: L -- Left heavier R -- Right heavier B -- Balance Example: L L B -- Counterfeit coin is among 1, 2, 7, 10  7 is lighter Binary Search

More Related