The Game of Nim - a math game of strategy using matchsticks! - Free Educational videos for Students in K-12

The Game of Nim - a math game of strategy using matchsticks! - By tecmath

Transcript


00:0-1	Good day and welcome to the Tech Math channel .
00:01	I'm josh today . I'm showing you the mathematical strategy
00:04	game nim It's a game that we play with matchsticks
00:06	or any counters and the aim of the game is
00:08	not to be left with the last match , Dick
00:10	. It's a great little game . And I'm going
00:12	to first , I'll show you how to play this
00:14	game and then I'm going to show you the strategy
00:16	that you can use , so you never lose this
00:19	game and it will drive your friends nuts . But
00:23	before I do that , this is a sponsored video
00:25	and as a message about my sponsor skill share .
00:29	So before we start , this video is a sponsor
00:31	video from the online learning community skill share . That's
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01:01	the video description below , and the great thing is
01:03	the 1st 1000 people to use this link will get
01:05	a free trial of skill share , premium membership .
01:07	This is a limited time offer , so check it
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01:13	. So back to the game of Nim . So
01:15	the set up for this game is as follows ,
01:17	we have four rows in in the first row we
01:19	have one matchstick in the second row we have three
01:23	matchsticks . In the third row we have five matchsticks
01:27	, and in the fourth row we have seven matchsticks
01:31	and set up . As you can see there ,
01:33	the game is played with two players taking turns where
01:36	each turn consists of taking any number of matchsticks from
01:39	a single row . Once again the aim not to
01:42	be left holding the very last matchstick . So playing
01:45	this game we could have a look as follows .
01:47	So first off , what happens is player one goes
01:50	through and could take any number of matchsticks from any
01:52	row , and they decide , for example , let's
01:55	take three matchsticks from row four . Okay , so
01:58	player two is now going to have their turn so
02:00	they can take any number of matchsticks from any row
02:03	, and they decide to take two matchsticks from the
02:05	second row and so on , and so forth .
02:07	As you can see , this person takes three .
02:11	This person takes to this person takes one . This
02:14	person takes one . This person takes to this person
02:18	takes one and then the loser is eventually left with
02:22	that single match Dick . So this video is not
02:24	just about telling you how to play the game of
02:26	Nim , but it's also going to be talking about
02:28	the mathematical strategy behind always winning the game of Nim
02:32	. And in case you're playing this game by yourself
02:35	, there is an online version of this game that
02:36	I'm going to put in the link . And interesting
02:38	enough , this game , not the one I'm linking
02:39	to of course , but the game of Nim was
02:42	one of the first computer games ever built in 1940
02:45	. The Nimble machine was displayed at the new york
02:47	World's Fair and apparently only a few people could beat
02:50	it . So how can you play this game and
02:53	win every single time ? Well , the winning strategy
02:56	, as you'd expect involves a little bit of maths
02:58	and I think the best way is to probably show
03:01	you so we're gonna start a game . As you
03:04	can see here , we have 135 and seven matchsticks
03:08	. Now the secret behind the strategy of playing this
03:10	game involves looking at ways for each row that we
03:14	can make the numbers using 42 and one through addition
03:19	. Okay , pretty easy to remember because double of
03:22	one is two and double of two is four .
03:24	So now we look at the first row , we
03:26	have one match here . This can be made up
03:29	of just one in this road . In the second
03:31	row we have three matches . This is made up
03:33	of two plus one in the third row we have
03:36	five matches . This is made up of four plus
03:39	one . And in the fourth row we have seven
03:42	matches . This is made up of 42 and one
03:46	. And now the trick of how you actually play
03:48	this game is pretty simple . The next thing what
03:49	you're going to do is you are going to pair
03:51	these up and obviously once again in your head ,
03:53	but it's not too bad to do . So we
03:55	have a one and a one , we have a
03:57	one and a one , we have a two and
03:59	a two here and we have a four and a
04:01	four . As you see these all pair up and
04:04	nothing is left over . This is said to have
04:07	a nim some it's equal to zero and this is
04:10	what you want to be leaving your opponent , You
04:13	want to be leaving them . This nim sum of
04:15	zero . So this is all paired up . So
04:18	always leave your opponent with this except at the very
04:21	end as you'll see and you'll win . So what
04:23	about I'll show you by playing this game through .
04:26	So let's continue this game . Obviously for the first
04:29	move , there is no way that you can leave
04:31	a name some of zero because you're starting with the
04:33	name some of zero . So you're going to a
04:35	state of non equilibrium , I guess you could think
04:37	, and that's why you don't want to be starting
04:39	your opponent not knowing this . However , goes first
04:42	and takes two matches from the fourth wrote . So
04:45	it leaves one match three match , five matches and
04:48	five matches . So now we can go through and
04:51	do the grouping so we can work out what to
04:53	leave our opponent . We have a one . We
04:55	have three matches here , which is made up of
04:57	21 We have five matches here , that's made up
05:00	of four and won five matches is made up of
05:03	four and one . So you can pretty easily see
05:05	which one you're gonna be getting rid of this one
05:07	here pairs . These guys here pair , these guys
05:10	here pair , we've got this to here . So
05:13	we want to be leaving a name some of zero
05:15	. We want everything to be paired up . The
05:16	easiest way is we're going to get rid of two
05:18	matches . So let's go through and do that and
05:22	this is what you would be leaving your opponent .
05:24	So let's just see what they do now . So
05:26	your opponent's gonna now just do whatever they do .
05:28	But you're in the winning position at the moment ,
05:30	no matter what they do , you can counter with
05:33	a move to put them back in the name some
05:35	of zero . So what they do is they go
05:37	through and take three matches from this third . Right
05:41	, okay . We have three matches from the third
05:43	row . So now we have 112 and five .
05:46	Let's let's write that down . We have 112 and
05:50	four plus one . Cool . Right , so now
05:54	let's work out what match to take ? We have
05:56	one and one here . And what we have here
05:58	, is that two of four and a one .
06:00	Now ? How can you go through and make these
06:02	numbers here ? So they're going to match up with
06:05	his two ? Well , if we take three from
06:08	this entire row here , what we're going to end
06:10	up with is five take three . We're gonna end
06:12	up with two matches . And then these guys will
06:15	pair up and we'll end up with a name some
06:17	of zero . So we would take three matches off
06:20	. Let's do that . And you can see now
06:22	what we've got left . This is what we have
06:24	. We have a one a one or 202 that's
06:28	made up of two there . Now . These guys
06:29	would pair up , everything's happy in the world ,
06:31	we've left them and dim sum of zero . So
06:34	now it's their turn . Okay , now your opponent
06:36	this stage , usually it's fun to watch them .
06:38	They're trying to scratch their head and work out what
06:40	they're gonna do . That kind of thinking they're still
06:42	in the game . You haven't told them they've lost
06:44	from the very first move and don't let them know
06:47	. All right , So what they're gonna do is
06:49	there is going to do some movement . Let's face
06:50	it , we know it's not going to matter .
06:53	Let's say they take one match from row one .
06:56	All right . What have we got now ? We
06:58	have one match here to here to here . We
07:02	can easily see the ones that are pairing up and
07:04	this is a bit of a thing caught often if
07:06	you have a symmetrical idea to and to , you
07:08	know , these guys going to pair up so you
07:10	just follow their move along . So how do we
07:12	now reach a name Summer Zero , We're going to
07:15	take one off that . So one off that second
07:19	road , we do that . What we end up
07:21	with is is here two matches and two matches .
07:25	So it's left to dim sum of zero . Now
07:28	it's their turn again . Usually this stage they're still
07:31	trying to figure out what they're going to do once
07:33	again , doesn't really matter . Still fun to watch
07:35	. Doesn't matter . But what they do is say
07:38	they take one match away and it's this one here
07:41	. Now , obviously what we're going to be left
07:43	with is two matches here and one match here .
07:46	Now watch out for this because you might think ,
07:48	OK , well what we do is we can take
07:50	off one match here and what we're going to be
07:53	left with is we are going to end up with
07:57	a name someone zero . And everything is good at
07:59	this stage . What you do is you have to
08:01	abandon leaving this name . Some funny enough , what
08:04	they've left you is a name someone zero at this
08:06	stage , but it doesn't matter because the game's almost
08:08	over . What's the object of the game is to
08:11	leave them with one match . So at this stage
08:13	, you don't want to snatch defeat from the jaws
08:15	of victory by making some silly move , like taking
08:18	one match away . That's not what we want to
08:19	be doing . We just take both matches away and
08:23	when we do that , we're going to leave them
08:24	with this last match here . And that means they're
08:27	going to lose the game . So that's how you
08:30	go about winning the game of Nim . All right
08:33	now , if you really want to try it out
08:35	, try it out on a friend . I recommend
08:37	go through a few rough games in your head first
08:39	. But as I said earlier in the description below
08:41	, I will leave a link on how to find
08:44	one of these games online . Anyway , that's how
08:46	you play the wonderful game of Nim . Before I
08:48	use particular strategy , I had a Bangladeshi guys showed
08:51	me how to play this . I used to work
08:53	with and he used to beat me every time and
08:55	it drove me up the wall . And the funny
08:57	thing is once I kind of worked it out ,
08:59	what I do is I do the same to my
09:01	students . They still get the idea . They can
09:03	win . You tell them you give them an A
09:05	or something like that . If they can just beat
09:07	your one game , it drives them up the wall
09:09	anyway . Once again , thanks to the sponsor of
09:11	this video skills share , I really recommend having a
09:14	look at them and see what you can discover .
09:16	The link is in the description , a big shout
09:18	out to my patrons and all you . Wonderful subscribers
09:21	. We're almost at a million . Right ? I
09:23	hope you like this video . Take care . Bye
00:0-1	.

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The Game of Nim - a math game of strategy using matchsticks! is a free educational video by tecmath.

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