The Numbers That Describe Themselves Math Riddle - Free Educational videos for Students in K-12

The Numbers That Describe Themselves Math Riddle - By tecmath

Transcript


00:0-1	Welcome to Take Math Channel . I'm josh in this
00:02	video . We're looking at the numbers that describe themselves
00:05	. These are autobiographical numbers . So an example ,
00:09	this one is as follows , A five digit autobiographical
00:12	number is 21,200 . And why is it said to
00:17	be autobiographical ? Pretty simple . It's digits describe how
00:21	many of each of those digits occur . I'll tell
00:23	you what I mean by this . So say there's
00:25	two here , we're gonna start out with how many
00:27	zeros there are in this particular number . There are
00:29	two zeros . The number describes that uh this is
00:32	how many ones there are ? There is 11 The
00:34	number describes that . There is two's there's two of
00:37	them that's described as well . How many threes are
00:39	there ? Well , there's zero and how many fours
00:42	? There are also zero . So , this number
00:44	describes itself describes how many of each digit are in
00:48	the number . So your challenge , can you find
00:51	the 10-digit autobiographical number , pause the video if you'd
00:55	like to give this problem to try and when you're
00:56	ready to see the solution started up again by the
00:59	way after the solution for this 10 digit number that
01:02	I'm gonna put out . I'm gonna include some other
01:04	length autobiographical numbers for you to try . So anyway
01:07	give this a go . So time's up . How
01:15	did you go ? Maybe it was easy . Maybe
01:17	not . As I said I'll explain in the solution
01:20	how to work this out and then I'm going to
01:21	give you some bonus autobiographical numbers for you to work
01:25	out a bit later . But before we get to
01:26	that I just like to take this opportunity to talk
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02:23	in the description below . Okay , back to our
02:25	10-digit autobiographical number . We're going to use a bit
02:28	of logic to work out what this particular number is
02:31	by Working with these digits here . Now the first
02:34	thing we can tell about this particular number is as
02:36	follows , we know that the sum of all the
02:39	digits in our number is going to be equal to
02:43	10 and we know that because there is a total
02:45	of 10 digits and as each digit here tells us
02:48	the number of times that digit occurs . The some
02:51	also has to be 10 , tells a number of
02:53	times of occurrence is 10 occurrences . Our total also
02:57	has to be 10 there and we can see this
02:59	using our five digit autobiographical number , 21,200 . And
03:04	if we have a look at this , it's five
03:05	digits long , but we also can see the two
03:07	plus one plus two . The number of times those
03:10	respective numbers occur or those respective digits occur equals a
03:14	total of five . So there we go straight away
03:18	. We know that the some of this number the
03:20	digits has to be tent . The next piece of
03:23	information we can work with is these last five digits
03:26	here . We know a couple of things about these
03:29	first off because now we know that we have a
03:31	limit of 10 that we can some these two we
03:34	know that there's not going to be too many of
03:36	these particular numbers . For example , if we had
03:38	more than actual two of these filled in , We
03:41	could have say 15 and 16 but that would give
03:43	us 11 digits that we'd have to contend with .
03:46	So do we know that most ? There's only gonna
03:49	be one of these numbers filled in . So it's
03:51	either going to be the following where we have four
03:54	lots of zero and one group of one or we
03:58	have five groups of zero . Now I can immediately
04:02	discount this five groups of 01 here . I'll show
04:05	you why If I was to fill these entirely up
04:08	with 000000 and we would have 50 and that's all
04:13	there were . Well number of Zeros I would put
04:16	down here would be a five then for my five
04:20	here I'd have to mark that in saying that we
04:22	have 15 there and it would be marked in here
04:25	. So we have a bit of an issue here
04:27	. We can't because we've already got a zero in
04:28	there and the same guys , we might have a
04:30	zero here but it's still gonna just affect it down
04:32	the line there . So we know straight away that
04:34	it's not five zeros there , we know that we
04:36	can only have one of these filled in . So
04:38	we know that it has to be four zeros and
04:41	one of them is going to be a one there
04:43	. So the next thing you can work on is
04:44	these five digits here . The first five digits ,
04:46	we know a couple of things about it . So
04:48	let's just go through these in order . How many
04:50	zeros do we have ? Well , we know it's
04:52	going to be a few , it's going to be
04:54	this number up here is going to be zeroes ,
04:56	otherwise we're going to get a number that's too big
04:58	too quickly . So we know that's going to be
04:59	5678 or 90 Is that we have in our 10
05:03	digit autobiographical number . However we have seen that it's
05:07	not five . So we know it's going to be
05:08	67 eight or 90 is that we have ? So
05:12	this is going to be a number greater than 66
05:16	or above . We know that we have at least
05:19	11 because we know that we have four zeros and
05:21	11 here . So we know that this number here
05:24	is at least going to be bigger than one .
05:28	We'll skip the two for the second and we'll have
05:29	a look at these threes and fours here . And
05:32	how many of those digits occur ? I can tell
05:34	you straight away there is zero fours and I know
05:36	this because there's six of these at least and at
05:38	least one of these and one of these . So
05:41	there's one down here as well . So six plus
05:43	one plus one is equal to 88 plus four is
05:46	12 , 8 plus three is 11 . Both of
05:49	these are too much . So these both have to
05:52	be zeros . Now , what we can do is
05:54	we can work out the number of twos . Once
05:57	again , we can't have too many twos here because
05:59	if we had to lots of 2 to 2 to
06:01	four plus that eight that we had , it would
06:03	be too many . So we can only have at
06:06	most one or we could have zero . Teus I'm
06:10	going to show you why it can't be zero .
06:12	If we were to put a zero in where the
06:14	twos are we to say , okay , there's no
06:15	twos , What does this tell us ? Well ,
06:17	we know straight away up here that we have four
06:20	zeros in this entire space here . So we have
06:24	four zeros plus three zeros . We know that we
06:27	have to have +70 So we put a one in
06:29	here and we put a seven with the zeros down
06:32	there . Seven plus one will put those zeros in
06:35	as well . 0007 plus one is equal to eight
06:38	. That means this would have to be a two
06:40	in here , but it's not a two is it
06:42	? Because we've said that we have no twos .
06:44	So what we can't have is we can't have this
06:48	being zero here , we have to have at least
06:50	12 and I can go as far as actually putting
06:53	that one in there right now . So now we
06:55	can work out how many ones we have . We
06:57	know we have at least one here and we have
07:00	a one up here . So how many ones do
07:02	we have ? We know this is not a one
07:03	and we know none of the other ones are a
07:04	one . So we know that this has to be
07:07	too All good . We know that one of the
07:10	ones is going to go up here . We have
07:11	a zero . So this is going to be one
07:12	plus one is two plus two is four . This
07:16	number here has to be a six . So this
07:19	will be the one which goes right there . The
07:21	rest of these will be equal to 00000 And that
07:27	is our 10 digit autobiographical number . Let's just have
07:30	a quick check of it . Okay , number of
07:32	Zeros . We have six of them . one ,
07:35	The number of ones we have to that's one to
07:37	their uh I'll get rid of that one up there
07:40	. The number of twos , we have one .
07:42	That's this one here . The number of threes we
07:43	have none . The number of fours we have none
07:46	. The number of five we have none . The
07:47	number of six is we have one . The number
07:50	of sevens . We have zero . Number eight ,
07:52	we have zero . The number of nines . We
07:53	have zero . We have a 10-digit autobiographical number .
07:57	And there you go . As I said , there's
07:59	some bonus problems coming . And I'm going to look
08:00	at some different autobiographical numbers after this . But first
08:03	let me take this opportunity to thank you for watching
08:05	my subscribers , my patrons and the sponsor of this
08:08	video data camp . And I recommend check him out
08:10	. As I said , sign up a free you've
08:11	got nothing to lose by developing the data skills .
08:14	You need to take your career to the next level
08:16	. The link is in the description . So now
08:19	let's get to the bonus questions . So these are
08:22	the bonus questions . We know that we have an
08:24	autobiographical number that is five digits long , that one
08:28	was 21,200 . We also know that we have just
08:33	worked out a 10 digit autobiographical number . That number
08:36	if I go off top my head with six billion
08:39	210 million and 1000 . There we go . Hopefully
08:45	I got that one correct . Okay , did you
08:47	know that there's some other autobiographical numbers and these are
08:51	what you are supposed to find right now ? The
08:53	first one , there are four digit ones . In
08:56	fact four digit ones . There are two of these
08:59	. Okay , so can you work at 24 digit
09:02	autobiographical numbers ? There is a seven digit autobiographical number
09:07	. There is an eight digit autobiographical number and there
09:10	is a nine digit autobiographical number . So can you
09:13	work these out ? I'm not gonna give you the
09:14	answers to these straight away because I'm not a very
09:16	nice guy . Put them in the comments Eventually ,
09:19	I'm going to put them in the description so you
09:21	can uh then go through and see these . But
09:24	for the start , not gonna do this for you
09:25	. I want you to go through and see if
09:27	you can discover a couple of these for yourself anyway
09:30	, thank you for watching . It's been a pleasure
09:33	to see you next time . Bye .

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