Where did the extra dollar come from? - By tecmath
Transcript
| 00:00 | Good day . Welcome to Tech Math channel . I'm | |
| 00:02 | josh . This problem has been touted as the world's | |
| 00:04 | toughest riddle in that way that Clickbait titles go see | |
| 00:07 | . What do you think this is the problem ? | |
| 00:10 | So I start with $50 from this . $50 I | |
| 00:14 | spent $20 so 50 take away 20 . It leaves | |
| 00:17 | me with a balance of $30 from this . $30 | |
| 00:20 | I spent $15.30 take away 15 . That leaves me | |
| 00:23 | with a balance of $15 from this balance of $15 | |
| 00:27 | . I spend $9.15 take away Nine . This leaves | |
| 00:30 | me with a balance of $6 and then finally I | |
| 00:34 | spend this last $6 which leaves me with a balance | |
| 00:37 | of nothing . Now I go through a total of | |
| 00:39 | the amount of money I've spent here , 20 plus | |
| 00:42 | 15 plus nine plus six . You'll see that . | |
| 00:44 | This sums up 2 $50 . If I didn't say | |
| 00:48 | my balance column here , 30 plus 15 is 45 | |
| 00:51 | plus six , This gives me an answer of $51 | |
| 00:55 | . So this is your problem . Where did this | |
| 00:57 | extra dollar come from ? Was started with 50 . | |
| 00:59 | I spent $50 here . But in the balance this | |
| 01:02 | adds up to 51 . Where did this extra dollar | |
| 01:04 | come from , pause this video . If you'd like | |
| 01:06 | to give this problem and try and when you're ready | |
| 01:08 | to see how to solve it , started up again | |
| 01:15 | . Yeah . Yeah . Mhm . Okay , time's | |
| 01:21 | up , geo did you manage to solve it ? | |
| 01:23 | Where did that extra dollar come from ? Well , | |
| 01:25 | here's the answer is going to get some anger in | |
| 01:27 | the comments , I'm sure , but it didn't come | |
| 01:28 | from anywhere . There is absolutely no relation between the | |
| 01:31 | total amount spent here and the total of the balance | |
| 01:34 | . This problem is fooling us into comparing the amount | |
| 01:37 | spent into something which is essentially meaningless . That is | |
| 01:40 | the total balance . But by having the totals of | |
| 01:42 | these columns really close to one another , it appears | |
| 01:45 | that the total balance here actually has a meaning which | |
| 01:48 | it doesn't . And I'll show you this right now | |
| 01:50 | , just by changing up the riddle a little bit | |
| 01:52 | and changing some of the figures involved . So if | |
| 01:54 | I was to get rid of the amount that we | |
| 01:55 | spend here and I'll get rid of our totals , | |
| 01:58 | okay , Say I spend $1.50 take away one . | |
| 02:02 | This would leave me with a balance of 49 . | |
| 02:05 | Okay , now what I do is I spend another | |
| 02:07 | dollar . Okay , so 49 take away one and | |
| 02:11 | now leads me with 48 you can see straight away | |
| 02:13 | there's no way that I'm going to get these guys | |
| 02:15 | eating up to 50 I've already passed 50 . And | |
| 02:17 | if I keep spending my $50.1 dollar at a time | |
| 02:20 | when my balance is going to go 49 48 47 | |
| 02:23 | 46 it's going to sum up to a number that's | |
| 02:25 | absolutely enormous way over the number 50 . So this | |
| 02:28 | is the thing , the spend column is always going | |
| 02:30 | to add up to the number 50 but the balance | |
| 02:32 | column won't . And adding the balance is a completely | |
| 02:35 | logical thing to do If you're trying to determine how | |
| 02:37 | much money you started with , I guess I'll give | |
| 02:40 | you one more example of where you might be able | |
| 02:41 | to see this , but maybe you'll see this straightaway | |
| 02:45 | . Say I got my $50 and I spent it | |
| 02:48 | all in one fell swoop $50 . Take away $50 | |
| 02:52 | . My balance is $0 . Now let's work out | |
| 02:54 | these totals . Well , the amount spent is $50 | |
| 02:57 | . No surprise there , but the balance is now | |
| 03:00 | $0 . This column here is always going to add | |
| 03:03 | up to 50 and this column here . Well , | |
| 03:05 | to sum it up actually doesn't really give us any | |
| 03:08 | meaningful information so it's a pointless exercise . And it's | |
| 03:11 | not always gonna up to 50 it's gonna add up | |
| 03:13 | from anywhere from zero right up to whatever the sum | |
| 03:16 | of all those 50 plus 49 plus data that are | |
| 03:20 | his . So that was today's problem . Let me | |
| 03:22 | know what you thought of it . I know a | |
| 03:23 | few people are going to get angry about that , | |
| 03:26 | but that's just the way it is . But I | |
| 03:27 | can tell you it's one of those ones , if | |
| 03:29 | you ask a lot of people they will spend their | |
| 03:31 | entire time getting confused about it because sometimes what we | |
| 03:34 | have to watch is actually what we are adding up | |
| 03:36 | . Whether they actually do mean anything . I think | |
| 03:38 | it's a great example of that anyway . Thank you | |
| 03:41 | for watching and I will see you next time . | |
| 03:43 | Bye . |
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