tag:blogger.com,1999:blog-5730391.post3792874318676035677..comments2022-01-26T18:27:08.951-08:00Comments on Blaine's Puzzle Blog: NPR Sunday Puzzle (Oct 19, 2014): Time To Flex Those Math MusclesBlainehttp://www.blogger.com/profile/06379274325110866036noreply@blogger.comBlogger153125tag:blogger.com,1999:blog-5730391.post-80473814777600012092014-10-27T14:23:05.994-07:002014-10-27T14:23:05.994-07:00The World Series question: to win the Series in 5...The World Series question: to win the Series in 5 games, your first inclination is C(5,4)=5. However, that includes the possibility of a 4 game sweep. The key to the answer is that to win the Series in 5 games, the last game won is the fifth game, with 3 wins (or equivalently, 1 loss) in the first 4 games. This equals C(4,3) = C4,1) = 4.<br /><br />The same logic applies to win the Series in 6 games and 7 games--3 victories in the first 5 games or 6 games, respectively (or equivalently, 2 or 3 losses in the first 5 or 6 games, respectively). In symbols, the numbers are C(5,3) = C(5,2)=10 and C(6,3) = 20, respectively, Thus, the number of ways of winning the Series in 4, 5, 6, and 7 games is 1, 4, 10, and 20, respectively. These translate to probabilities of 1/35, 4/35, 10/35, and 20/35, respectively. <br /><br />In 2003, a Harvard Math Professor (whose name was never revealed for obvious reasons--read on) committed a worse error than Bill Buckner's famous 1986 error, by stating that these probabilities were 2/16. 4/16, 5/16, and 5/16. I can only wonder with results like this, if he so-called math Professor obtained his Ph.D. from one of those bogus diploma mills that grants degrees to everyone who forks over the $, no questions asked.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5730391.post-91773636272240401972014-10-27T14:11:11.209-07:002014-10-27T14:11:11.209-07:00If a team wins 4 games, it does not win 3 games, m...If a team wins 4 games, it does not win 3 games, making C(7,4) = C(7,3). More generally, C(n,r) means picking r objects from n, leaving n-r objects not picked. If you reversed roles, you'd be picking n-4 objects and leaving n objects not picked--thus (C(n,r)=C(n,n-r). No numbers or algebra was used in this explanation, nor were any animals harmed in doing so.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5730391.post-72487650201189655222014-10-26T07:41:49.526-07:002014-10-26T07:41:49.526-07:00I've updated the answer to Will's accepted...I've updated the answer to Will's accepted answer of 21. I applaud those that figured out 21 when I was content to stop on the first answer that worked.Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-765681112277827652014-10-26T07:08:06.544-07:002014-10-26T07:08:06.544-07:00stare decisisstare decisisbenmar12001https://www.blogger.com/profile/02721420444783718903noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-3751048197330748422014-10-26T06:01:08.889-07:002014-10-26T06:01:08.889-07:00My sediments, exactly,My sediments, exactly,zeke creekhttps://www.blogger.com/profile/12559686966843380823noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-38999318013869558072014-10-26T05:58:44.651-07:002014-10-26T05:58:44.651-07:00Agreed, Will seems to love puzzles of this sort, a...Agreed, Will seems to love puzzles of this sort, and we have had many closely related to it.<br /><br />So easy, I was writing down the answer even as he re-stated it as usual on the air.Bob Kerfufflehttps://www.blogger.com/profile/02615811802419025933noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-73975133132885294352014-10-26T05:38:39.774-07:002014-10-26T05:38:39.774-07:00I know!I know!Word Womanhttps://www.blogger.com/profile/15491300694641304112noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-79029960682547211962014-10-26T05:19:06.257-07:002014-10-26T05:19:06.257-07:00Again!?!?Again!?!?janhttps://www.blogger.com/profile/05927176621372532733noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-68966266639550232014-10-26T05:15:22.916-07:002014-10-26T05:15:22.916-07:00Next week's challenge: This challenge comes fr...Next week's challenge: This challenge comes from listener Mike Reiss, who's a writer for The Simpsons. Name a well-known TV actress of the past. Put an R between her first and last names. Then read the result backward. The result will be an order Dr. Frankenstein might give to Igor. Who is the actress, and what is the order?janhttps://www.blogger.com/profile/05927176621372532733noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-1407657620960858052014-10-26T04:15:03.822-07:002014-10-26T04:15:03.822-07:00My first solve was using the Johari Window with bl...My first solve was using the Johari Window with blue and brown with a blue eye recessive gene sets.zeke creekhttps://www.blogger.com/profile/12559686966843380823noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-52375906951521404182014-10-26T04:06:07.936-07:002014-10-26T04:06:07.936-07:00Half of the students were sent home with pink eye ...Half of the students were sent home with pink eye and all the rest has blue eyes. Perhaps this wasn't so brilliant.zeke creekhttps://www.blogger.com/profile/12559686966843380823noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-91813128650133697622014-10-26T04:03:36.887-07:002014-10-26T04:03:36.887-07:00btw, I used 3 Equals and 1 Sweet-n-lo for the &quo...btw, I used 3 Equals and 1 Sweet-n-lo for the "hat" proof.zeke creekhttps://www.blogger.com/profile/12559686966843380823noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-49124160546295925532014-10-25T20:45:44.737-07:002014-10-25T20:45:44.737-07:00If the classroom has 15 out of 21 students with bl...If the classroom has 15 out of 21 students with blue eyes, it is already not typical. The problem could have asked about pairs with brown eyes, rather than blue, for it to have had a chance to be a typical classroom.Bryanhttps://www.blogger.com/profile/11149525317349695429noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-21872736607788365432014-10-25T20:33:43.040-07:002014-10-25T20:33:43.040-07:00I think I should also add that if WS was going to ...I think I should also add that if WS was going to insist on the answer of 21 only, then he should have stated the classroom was filled with students. Many puzzles imply something such as a room being filled, but the answer turns out to be much different, requiring the solver to think outside the proverbial box, as it were. WS only stated the classroom was typical, but gave no factual evidence to indicate anything more regarding its content such as the size of the class itself, or the percentage of students present. skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-2798249631019159662014-10-25T20:22:15.190-07:002014-10-25T20:22:15.190-07:00Both answers are perfectly correct. If you prefer ...Both answers are perfectly correct. If you prefer a mathematical puzzle, then you may prefer the answer of 21, but if you are more inclined toward using logic as your means of discerning an answer, then 4 is the obvious answer. I prefer the latter as I am not schooled at math, but I enjoy solving problems using my intellect. Were I proficient at math I would still prefer 4 as the better answer. I cannot speak for Blaine, but I do know he enjoys math puzzles, however he is obviously a logical thinker and has no reason to back away from his pristine answer of 4. To my way of thinking it is far more satisfying to lie in bed, as I did, and solve this puzzle with nothing but my reasoning instead of resorting to a calculator to do the work. Insisting that only one of these answers can be the correct one is, in my opinion, both arrogant and obnoxious on the part of Mr. Shortz.skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-67331263296910515842014-10-25T19:30:53.090-07:002014-10-25T19:30:53.090-07:00Blaine,
I was a bit surprised last Thursday when ...Blaine,<br /><br />I was a bit surprised last Thursday when you placed your answer of 4 at the beginning. I'm even more surprised now that your answer of 4 <b><i>remains</i></b> at the top of this blog long after even when many of us have identified a class size of 21 as the expected answer; especially since this week's chosen winner, Jake, says of Will that "He doesn't accept 4 kids".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5730391.post-52887787231836351402014-10-25T19:21:22.207-07:002014-10-25T19:21:22.207-07:00How about a big lecture class with 697 students, 4...How about a big lecture class with 697 students, 493 with blue eyes? Or maybe a MOOC with 4060 students with 2871 blue-eyes students? <br /><br />With N students there are N*(N-1)/2 pairs. So if you have N students with blue eyes and M students total, the odds of getting a pair with blue eyes is N*(N-1)/(M*(M-1)). Bryanhttps://www.blogger.com/profile/11149525317349695429noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-25921396049982768542014-10-25T13:49:48.625-07:002014-10-25T13:49:48.625-07:00That's what Jake said.That's what Jake said.Paulhttps://www.blogger.com/profile/11114786604125384958noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-15626542779994087242014-10-25T12:52:07.487-07:002014-10-25T12:52:07.487-07:00But Iran/Riga/Iraq was accepted as correct, just d...But Iran/Riga/Iraq was accepted as correct, just deemed less elegant. I think 4 this week will not be accepted as correct. Rakewellhttps://www.blogger.com/profile/15873391354585352712noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-65046156796124408642014-10-25T11:47:27.709-07:002014-10-25T11:47:27.709-07:00Optimization may very well be in the eyes of the r...Optimization may very well be in the eyes of the regulator.Paulhttps://www.blogger.com/profile/11114786604125384958noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-69192705474040269362014-10-25T10:28:15.414-07:002014-10-25T10:28:15.414-07:00I have a math puzzle for you all to consider.
If ...I have a math puzzle for you all to consider.<br /><br />If I were to take this puzzle to a typical PTA meeting here in Seattle, how long would it take for the laughter to subside when they learn the answer is a class size of less than thirty students?skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-27635611192700554072014-10-25T10:20:13.541-07:002014-10-25T10:20:13.541-07:00 Agreed, zeke creek. The kindergartners who te... Agreed, zeke creek. The kindergartners who teach me on Science Fridays number 10. My friend, Lisa, teaches science in classrooms of 4, 3, and 1 student(s).<br /><br /> The average private elementary school size in some countries is 11 or less. Word Womanhttps://www.blogger.com/profile/15491300694641304112noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-26711992477430852382014-10-25T09:43:54.152-07:002014-10-25T09:43:54.152-07:00Being a promoter of quality learning I find the c...Being a promoter of quality learning I find the class size of 21 to be abnormal.zeke creekhttps://www.blogger.com/profile/12559686966843380823noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-23916915756686222522014-10-24T21:01:21.649-07:002014-10-24T21:01:21.649-07:003 does not even come close to working. There would...3 does not even come close to working. There would be only one chance of coming up with Blue/Blue, but two chances of Brown/Blue.<br /><br />If our winner this week is correct and WS does not even mention 4 as being the answer, then he has really slipped even further in my disrespect for his sloppy work. It now appears he was presenting us with more of a mathematical puzzle than a logic puzzle, which is what I, and apparently most others, assumed it to be. I suspect he again, as usual, did not check his possibilities and just assumed the answer would be the one he has so arrogantly chosen over all other equally correct answers. This guy is really an egotistical jerk as I have been informed is the case from a third party who should know.skydiveboyhttps://www.blogger.com/profile/17174073226290431753noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-23403386468419587622014-10-24T20:37:57.446-07:002014-10-24T20:37:57.446-07:00I said 3 - I currently believe I am one of the 190...I said 3 - I currently believe I am one of the 190 - but Will has a grudge against me - going back to that night in Juarez - tequila - ping pong balls... ' nuff said.TomRhttps://www.blogger.com/profile/10000427318383579622noreply@blogger.com