Nine Penny Problem with The Two Pan Balance: You have nine...

Nine Penny Problem with The Two Pan Balance: You have nine pennies. Eight of the pennies are post 1982 dated, therefore they weight 2.500 grams eash. You have one penny with a 1974 mint date and it weighs 3.100 grams. You need to design and write the directions for an experiment on how you would use the above balance to find 100% of the time, the heavier 1974 penny: 1.Write the directions below as steps Only what is the number of weighing needed in your this procedure below: Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: How many weighing would use use maximum to sove the problem: One Two Three Four Five 2. Now rewrite the experiment so that it will take a different Number of weighings Write the directions below as steps Only what is minimal needed) in you procedure: Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7: Step 8: How many weighing would use use maximum to sove the problem: One Two Three Four Five 3. Now try to rewrite the experiment so that it will take a different Number of weighings than #1 or #2

Transcript

00:02 All right, so you're going, you're trying to figure out what would be a good way to figure out which were pennies that came from before 1974 and the ones that came after that, it looks like.

00:18 So you're trying to pick out which ones were the heavier in 1974 pennies 100 % of the time without looking at them, i assume.

00:26 We can just read the data on them and know that they were the 1974 pennies.

00:31 But without looking at the actual date, let's see what we can come up with.

00:37 So if you have 10 pennies, oh, you have nine pennies.

00:44 So i would just weigh this first time around, weigh each penny individually, until you find the one penny that has a weight of 2 .5.

01:12 0 grams.

01:13 So that might be the first one that you do.

01:15 It might be the last one, but you can get by with how many wings would you use maximum to solve the problem? well, you would need to weigh it individually.

01:27 You could have nine different weights.

01:29 That would be the, or eight would be the maximum here.

01:33 Well, that doesn't look like one that they want us to do.

01:37 But i just didn't want to use the eat the ease or the ones that had less weights.

01:43 It looks like you have to do this over and over again.

01:45 It looks like where you're going to come up with different procedures.

01:53 So i guess the purpose of your, of this activity is to rewrite procedures until you get some more concise procedures that don't take as many steps is what i'm assuming the activity is about.

02:13 So the very first time, i would just say step one way first penny out of the pile.

02:22 If you want, you could say, let's weigh two pennies.

02:27 So weigh two pennies at a time until you find the two pennies, find the penny that has a weight of 2 .5.

02:52 So that would, when you weigh two pennies, that should be less than 6 .2.

03:00 0 .00 grams when two pennies are weighed.

03:06 So i don't want to write the procedure directly for you, but i can talk it through and then you can come up with your own words.

03:13 So weigh two pennies at a time until you find the penny that has a weight of 2 .5 grams.

03:18 That would be the penny that's going to be in the in a pair of pennies that weighs less than 2.

03:26 Or 6 .2.

03:27 Then all i have to do is weigh those two pennies.

03:32 To find which one it was that is the non -1974 one.

03:37 So that one, you could probably get by with, let's see, you would need five for this procedure.

03:48 So i think that would be good.

03:50 We want to be able to save our best ideas until later.

03:54 So five is that going to be the maximum that you may only take two weights, but you would have to, the maximum would be five.

04:04 All right, so let's see here...

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