bonanova Posted February 3, 2011 Report Share Posted February 3, 2011 It's finals day at the chem lab. Your instructor has placed on your table 13 numbered beakers containing colorless and odorless liquids. "The contents of one and only one beaker are slightly acidic," he tells you, "the others are neutral; they have a pH of exactly 7." He also hands you four clean flasks, labeled A, B, C and D. Put anything you like from the beakers into these flasks, and I'll test all four of them for acidity. When I give you those results, you must then tell me which of the 13 beakers is acidic. You never got an easier A. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 Add some quantities of liquid from each beaker to A, B, C and D. We need to ensure that a certain result identifies one of the 13 beaker uniquely. Easiest way is to label the beakers 1 - 13, represent each as a four digit binary (corresponding to A, B, C and D), and add some quantity of the fluid for those flasks which correspond to a binary bit '1'. E.g, Beaker 1 = 0001 => Add some of the liquid to flask D Beaker 2 = 0010 => Add some of the liquid to flask C Beaker 3 = 0011 => Add some of the liquid to flasks C and D Beaker 4 = 0100 => Add some of the liquid to flask B .. so on Beaker 13 = 1101 => Add some of the liquid to flasks A, B and D Now based on the result of which of the flasks are seen as acidic, we can tell which beaker was acidic. I'm assuming that the dilution of the liquid still retains enough acidity to pass the litmus test.. Quote Link to comment Share on other sites More sharing options...
0 soop Posted February 3, 2011 Report Share Posted February 3, 2011 reserve one beaker. Split the remaining 12 into 2 groups of 6. pour all of 1 group into the first beaker. If PH is neutral, disregard the entire 6, if acidic, your acid is present here. next, take 3 beakers (from the tested 6 if acid, from the untestes if not) and pour them into flask 2, then test. At this point, you will have narrowed it down to 4 beakers, and you have 2 flasks left. pour 2 into flask 3, and depending on the result, one more into beaker 4. Trial and error. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 reserve one beaker. Split the remaining 12 into 2 groups of 6. pour all of 1 group into the first beaker. If PH is neutral, disregard the entire 6, if acidic, your acid is present here. next, take 3 beakers (from the tested 6 if acid, from the untestes if not) and pour them into flask 2, then test. At this point, you will have narrowed it down to 4 beakers, and you have 2 flasks left. pour 2 into flask 3, and depending on the result, one more into beaker 4. Trial and error. i concur with this method Quote Link to comment Share on other sites More sharing options...
0 Aaryan Posted February 3, 2011 Report Share Posted February 3, 2011 i concur with this method But you can only test with the beakers once. Not multiple times. I think methinks got it. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 It's finals day at the chem lab. Your instructor has placed on your table 13 numbered beakers containing colorless and odorless liquids. "The contents of one and only one beaker are slightly acidic," he tells you, "the others are neutral; they have a pH of exactly 7." He also hands you four clean flasks, labeled A, B, C and D. Put anything you like from the beakers into these flasks, and I'll test all four of them for acidity. When I give you those results, you must then tell me which of the 13 beakers is acidic. You never got an easier A. 1. Paste paper chits containing the numbers 1, 2, 4 and 8 on flasks A, B, C and D respectively 2. To the flask 'A', labelled '1', add liquids from flasks 1,3,5,7,9,11 and 13. 3. To the flask 'B', labelled '2', add liquids from flasks 2,3,6,7,10 and 11. 4. To the flask 'C', labelled '4', add liquids from flasks 4,5,6,7,12 and 13. 5. To the flask 'D', labelled '8', add liquids from flasks 8,9,10,11,12 and 13. 6. Do acid test on all the four flasks. 7. Simply add up the label numbers of all the flasks whose acid test is positive. You have the beaker number containing the acid AND your A!!! Test run: Supposing the beaker number 7 has the acid; the acid test will be positive in the first 3 flasks. Add their numbers!! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 You would be able to ace this test had there been 14 beakers. Label the beakers 1 - 14 and the Flasks 1 - 4 Place some of the liquid from the beakers into the flasks so that each beaker is in a unique configuration of flasks, as follows: Place liquid from beaker number: 1 into flask 1 2 into flask 2 3 into flask 3 4 into flask 4 5 into flasks 1 and 2 6 into flasks 1 and 3 7 into flasks 1 and 4 8 into flasks 2 and 3 9 into flasks 2 and 4 10 into flasks 3 and 4 11 into flasks 1, 2 and 3 12 into flasks 1, 3 and 4 13 into flasks 2, 3 and 4 14 does not get used When you learn which flasks have a PH greater than 7 you will easily be able to determine which beaker had the acid. Examples: If flask 3 is the only acidic one, the acidic beaker is #3 If flasks 2 and 4 are the only acidic ones, the acidic beaker is #9 If none of the flasks are acidic then the acidic beaker is #14 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 But you can only test with the beakers once. Not multiple times. I think methinks got it. I don't believe it states you have to test all four at one time, so I see no reason the "trial and error" method would fail? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 3, 2011 Report Share Posted February 3, 2011 I don't believe it states you have to test all four at one time, so I see no reason the "trial and error" method would fail? Look at the question carefully: the instructor asks the student to put anything he wants into the flasks, and then he tests them for acidity. Put in another way, all the four flasks would be taken away by the instructor and tested for acidity, and the student is just given the results; with the results the student should point out the acid pot. I don't think you will pass, let alone get an A, if you say, after the first test, "Hold on dude, let me try this other combination"... There's thus no scope for the trial-and-error method... Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted February 3, 2011 Author Report Share Posted February 3, 2011 Yekangi is correct. The wording of the OP " ... I'll test all four of them for acidity. When I give you those results, you must then tell me ... " precludes some of the answers given. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 4, 2011 Report Share Posted February 4, 2011 actually methinks answer is also correct, just that he was talking Binary compared to English by Yekangi Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 4, 2011 Report Share Posted February 4, 2011 So i haven't really worked this out in my head yet, but let's suppose that the "teacher" is using a pH meter, and will give you an accurate pH reading from each flask (let's stick to the idea that all four have to be tested at the same time). Does the Methinks and Yekangi answer still hold true for any of the given 13 beakers, as one flask will contain an uneven amount of liquid? (Keep in mind we have no measuring devices on hand) Quote Link to comment Share on other sites More sharing options...
0 wolfgang Posted February 4, 2011 Report Share Posted February 4, 2011 I concur with the binary solution,it is the best answer as I think. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 4, 2011 Report Share Posted February 4, 2011 (edited) You would be able to ace this test had there been 14 beakers. Label the beakers 1 - 14 and the Flasks 1 - 4 Place some of the liquid from the beakers into the flasks so that each beaker is in a unique configuration of flasks, as follows: Place liquid from beaker number: 1 into flask 1 2 into flask 2 3 into flask 3 4 into flask 4 5 into flasks 1 and 2 6 into flasks 1 and 3 7 into flasks 1 and 4 8 into flasks 2 and 3 9 into flasks 2 and 4 10 into flasks 3 and 4 11 into flasks 1, 2 and 3 12 into flasks 1, 3 and 4 13 into flasks 2, 3 and 4 14 does not get used When you learn which flasks have a PH greater than 7 you will easily be able to determine which beaker had the acid. Examples: If flask 3 is the only acidic one, the acidic beaker is #3 If flasks 2 and 4 are the only acidic ones, the acidic beaker is #9 If none of the flasks are acidic then the acidic beaker is #14 Since there are 16 unique 4-digit binary numbers (including 0000), you could correctly identify the beaker that contains the acid even if there were 16 of them. Just do the same as before, with this little addition: Place liquid from beaker number: 14 into 1, 2, and 4 15 into 1, 2, 3, and 4 16 does not get used Or you could take a sip of each one to see which has a little bite to it. I just saw Yekangi's post and it works even better for doing 16 beakers. 1. Paste paper chits containing the numbers 1, 2, 4 and 8 on flasks A, B, C and D respectively 2. To the flask 'A', labelled '1', add liquids from flasks 1,3,5,7,9,11,13, and 15. 3. To the flask 'B', labelled '2', add liquids from flasks 2,3,6,7,10,11,14, and 15. 4. To the flask 'C', labelled '4', add liquids from flasks 4,5,6,7,12,13,14, and 15. 5. To the flask 'D', labelled '8', add liquids from flasks 8,9,10,11,12,13,14, and 15. 6. Do acid test on all the four flasks. 7. Simply add up the label numbers of all the flasks whose acid test is positive and you have the beaker number containing the acid!! 8. If none are positive, it's beaker 16. Edited February 4, 2011 by Louie Quote Link to comment Share on other sites More sharing options...
Question
bonanova
It's finals day at the chem lab.
Your instructor has placed on your table 13 numbered beakers containing colorless and odorless liquids.
"The contents of one and only one beaker are slightly acidic," he tells you, "the others are neutral; they have a pH of exactly 7."
He also hands you four clean flasks, labeled A, B, C and D.
Put anything you like from the beakers into these flasks, and I'll test all four of them for acidity.
When I give you those results, you must then tell me which of the 13 beakers is acidic.
You never got an easier A.
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