sepultallica Posted July 24, 2003 Share Posted July 24, 2003 i couldn't find where to put this one so i put it here. there is a math problem that i had heard once before that puzzled me. i'm not a math genious and hell, i have a hard time understanding algebra at times. the only way i can explain this one is by telling the story as i heard it. i haven't tried to find an eaisier way of explaining it so here goes. bear with me. three men enter a hotel and ask a clerk for a room for the night the clerk tells them that the cost for the room is $30.00. each of the three pays $10.00 (totalling $30.00). the manager later sees the guest book and realizes that he know these men and decides to give them a discount. he tells the clerk to refund the guys a total of $5.00. the clerk takes out $5.00 and thinks to himself, how do i divide $5.00 between three people? ultimately, he decides to give the guys $1.00 each ($3.00 total) and keep $2.00 (totalling to $5.00 as the manager requested). where the problem occurs is when you try to add it all together and you try to muliply and blah blah blah. if each paid $10.00 (totalling $30.00) and was refunded $1.00, you would get $27.00 (10x3=30. 10-1=9. 9x3=27) you then add that to the $2.00 that the clerk kept for himself to try to didvide things evenly (27+2=29). where did the last dollar go to? what is this principle called? is there any research on this? what's the deal here? can someone explain this to me? Link to comment Share on other sites More sharing options...
NavajoEverclear Posted July 24, 2003 Share Posted July 24, 2003 thats a lot relating to daves current post, i've heard that story before. As i remember it is a flaw in our system of math, but i'm not sure if i'm smart enough to explain how or why. Or maybe i just haven't thought hard enough, i'll tell you if i figure it out. How old are you? In 7th grade i stayed after school everyday for algebra help (we did prealgebra in 6th at my elementary), and now i'm doing (recently i did actually(its summer))just fine in precalculus, going onto calculus next year (11th). I'm sure you will figure it out if you work hard enough. Work is what makes the difference, I got Cs and Ds in 9th (in math) and just decided to work harder this year and i got Bs, could have probably got As if i wanted to, but to be honost i didn't think it was worth it, we'll see what happens next year. I do remember beginning algebra was the hardest though, but once you get a hang of it, everything then on will just be matter of how you are willing to work. Link to comment Share on other sites More sharing options...
frostyburn Posted July 24, 2003 Share Posted July 24, 2003 If they each got $1 back, they each paid $9 for the room (a total of $27). Add the $1 they each received back (a total of $3) from the boy ($3 + $27), and you have the $30. Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 Originally posted by NavajoEverclear thats a lot relating to daves current post, i've heard that story before. As i remember it is a flaw in our system of math, but i'm not sure if i'm smart enough to explain how or why. Or maybe i just haven't thought hard enough, i'll tell you if i figure it out. How old are you? In 7th grade i stayed after school everyday for algebra help (we did prealgebra in 6th at my elementary), and now i'm doing (recently i did actually(its summer))just fine in precalculus, going onto calculus next year (11th). I'm sure you will figure it out if you work hard enough. Work is what makes the difference i'm 25. i also don't have the luxury of sitting down and trying to figure this out. i have a full time plus job, a girlfriend that nags, and i'm a musician. i don't have time to figure stuff out. i sure as hell wasn't going to stay after school and donate my time to do something i didn't like. but now that i'm older, i'm a little more interested. i would like to take the time to figure it out. i know algebra, and calculus although i know that i would be extremely rusty. mathematics and science are interests of mine although they are not priorities for me. Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 Originally posted by sepultallica where did the last dollar go to? what is this principle called? is there any research on this? what's the deal here? can someone explain this to me? The principle is called 'adding it up wrong'. The $30 is made from the $9 they paid and the $1 they each received, it's just worded to deliberately confuse. (The $2 is taken from the 9's) Reword it to be 1 person who pays $30 and gets $3 back. It's pretty obvious. Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 Originally posted by MrL_JaKiri The principle is called 'adding it up wrong'. The $30 is made from the $9 they paid and the $1 they each received, it's just worded to deliberately confuse. (The $2 is taken from the 9's) Reword it to be 1 person who pays $30 and gets $3 back. It's pretty obvious. it's obvious if you add it the other way but at the same time if you calculate it the way i explained it it comes out wrong even though it shouldn't be. you have all the same factors involved your'e just approaching it differently. it's like saying 9x2=18 and 9+9=18. you are making the same calculation but choosing a different path only with my example, something gets srewed up. besides, your response didn't make that much sense to me. Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 Originally posted by sepultallica it's obvious if you add it the other way but at the same time if you calculate it the way i explained it it comes out wrong even though it shouldn't be. you have all the same factors involved your'e just approaching it differently. it's like saying 9x2=18 and 9+9=18. you are making the same calculation but choosing a different path only with my example, something gets srewed up. besides, your response didn't make that much sense to me. The point is it's NOT the same calculation. The question is more like saying '9x2 = 18, but 9 + 8 = 17 WHERE'S THE EXTRA ONE GONE?'. Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 even though all the same factors are involved in the calculation? Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 They're not though. The $27 is in a different calculation from the $2. One calculation is what they paid + what they received back (27 + 3 =30), the other is what they all have NOW (25 [manager], 2 [boy], 3 [guys] = 30) Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 ok then, suppose i wanted to look at each individual and total it that way. there should be nothing wrong with that. lets look at it. 1. 3 pay ten each 3x10=30 correct? 2. 5 is deducted from the total 30-5=25 correct? 3. of that 5 deducted, each that put 10 recieve 1 back 10-1=9 correct? 4. of the 5 deducted, we deducted three to reimburese leaving us with 2 from the five 5-3=2 correct? 5. in reality, if we were to sum up what each paid individually it would total to 9 each according to #3. 6. so if they only paid 9 each and 9x3=27 and the clerk kept 2, then you are still short. i bet you can walk in to a store and come out with more money than what you came in with. just gots to figure it out. there has to have been some research done on this somewhere. Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 Originally posted by NavajoEverclear thats a lot relating to daves current post what post is that? Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 No, you're wrong. It's just a TRICK. No research has EVEN been done on it, and none EVER WILL. What you're saying is that because of some mystery of adding up, a dollar bill vanishes into the aether! Link to comment Share on other sites More sharing options...
sepultallica Posted July 24, 2003 Author Share Posted July 24, 2003 it's not a trick, it's a flaw. a trick would be making the dollar vanish in thin air. a mathematical flaw would be something like what is described above. i find it hard to believe that this is the first time this has been brought up and that research hasn't been done on it. i would think that there could be serious reprecussions if this wasn't considered in certain calculations and theories. Link to comment Share on other sites More sharing options...
JaKiri Posted July 24, 2003 Share Posted July 24, 2003 Originally posted by sepultallica it's not a trick, it's a flaw. a trick would be making the dollar vanish in thin air. a mathematical flaw would be something like what is described above. i find it hard to believe that this is the first time this has been brought up and that research hasn't been done on it. i would think that there could be serious reprecussions if this wasn't considered in certain calculations and theories. No research has ever been done on it. No research WILL ever be done on it. This is because it's not a flaw in mathematics, it's a flaw in the person adding up; I've shown how the $30 is reached using both sets of values, and there is no argument against it, only ignorance (as you appear to be doing). This is not the first time I've seen it. This is not the 10th time I've seen it. For god's sake, I found it in a book of mathematical tricks and puzzles from the 1960's, it's hardly NEW. Thread over. Link to comment Share on other sites More sharing options...
Dave Posted July 24, 2003 Share Posted July 24, 2003 There is a difference between a trick and a flaw. A piece of 'trick' mathematics will try to convince the reader that there is a flaw in the mathematical system by falsely 'proving' something (like I 'proved' 1=9 in the other thread). This is NOT a flaw. I posted that particular thread so that I could get people to think a bit and say 'oh yeah, that's neat' or whatever. If I was trying to show you all that the system of trigonometric identities is wrong, then I would have posted a conclusive proof. The particular post is wasn't posted in that fashion. I mean, clearly it's just taking the wrong sign on a square root. blah. Link to comment Share on other sites More sharing options...
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