# The Game of Nim – a math game of strategy using matchsticks!

tecmath

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The game of nim is an easy to learn math strategy game, that can be played anywhere with matchsticks, rocks, twigs….

But best of all, whilst it looks fair, there is a math strategy you can employ to win everytime!

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15.04.2022

When I was attending college, I actually made a whole spreadsheet with all of the possible moves and combinations for both this version and the simplified version. It includes which moves to counter each opponent's move and which moves lead to loss of the game

Here's the strategy I've found to win any game, uses no maths.

On their first move, if they take one card, take away one card from any other row (but not the same row!). Then if they take one card from 1 of the 2 untouched rows, take one card from the final untouched row.

From this point on, or if they had done anything else for the earlier moves, you can always reduce it to the following 5 winning patterns on your current move.

1. The 1-1-1 pattern

2. The rectangle pattern (2-2, 3-3, 4-4, or 5-5)

3. Rectangle with a 1-1 (1-1-2-2, 1-1-3-3, 1-1-4-4, or 1-1-5-5)

4. The 1-2-3 pattern

5. The 1-4-5 pattern

Once you get it to one of these patterns, you just keep reducing it to another winning pattern until you win. With a bit of practice you can figure out your next move almost instantly, at most within 5 seconds.

It's teachers like you that just 😢😢😢😢😢😢ruin my d*** life

7:30 what if they just took 3?

So basically if XOR of number of matchsticks in each rows is 0, then the player who plays second wins else the player who starts wins.

There is a payment of this game ?

I found out about Nim in my maths class. It was the last day before Christmas so we had a sort of ‘Nim tournament’. I won. And not just slightly, I completely blew the rest of the class out of the water. 2nd, 3rd, 4th and 5th were all within a few points from eachother (5th with approx. 1082 points and 2nd with approx. 1086). But I had 1156 points. (Keep in mind we started on 1000 points, if we lost a game we lost points but if we won we gained points, meaning I actually won by at least 55%). To them, I was basically a nimatron / this website. Which is why It’s so frustrating when I repeatedly lost against that site you linked in the description. I must of seen the “Sorry… I won!” Pop up at least 100 times. The only way I can win is by opening the page in another tab, pressing “pc move” and mirroring it on the original tab, pressing “pc move” again and mirroring the move on the other tab. Repeat the process and you have the computer playing another computer which is a clone of itself. One of them will win and you get the “congratulations, you won!!!!!!!!!!!!!!!!”.

What if we start the game first?

This is a long winded way of giving a winning tactic. In NIM you have to take the final pin. It is far easier to just make whatever number your opponent takes up to four. I.E. opponent takes 2 you take 2, they take 1 you take 3, they take 3 you take 1.

Nine Inch Males 😂

I remember playing this game in middle school in math we had a whole tournament and everything and I got 2nd man this game was fun cuz kids didn't know what they were doing but I lost cuz I had to go first and the other dude knew how to win too

Does techmath reply 🙂

YES

thank you sir

I’m good at maths

I watched this version of NIM on Mathologer's channel but you have the better accent

Oh hell yeah

Thank u so much because of all your videos i passed my math ged 🙏Thanks!!!

Is the outcome different if you go first?

I wonder, is Mathologer smarter, or you?

Also, I think you would win in a fight.

1milliom near. …

❤❤from india

AYYY YES IM HAPPY YA GOT ADS MATE KEEP IT UP AND MAKE THE MONEY LAST!

what if they make you start first?

LOVE the channel! I was wondering, do you have any tips for solving algebra fraction problems? like x/2 + x/6=8?

Do a face reveal

Yay you’re still alive and you’re doing well glad to know

i need help with multiplication and division of integers pleas help me if you did a video tag me with the video

Ou

Amazing…..

TY.

/

Its nice you said 1000 people like eveybdoy to have a chance which isgood for people to have a chance oof it was a few years ago

Edit: it was 3months ago well if you used it for free congrats 🙂

I love that little laughs when you find number that isn’t in pairs 😂

Thanks for explanation, I have to teach kids this game on math fair in two days

What if we take 3 matchs off the last line at the biggining

7:30 Soft disagree on the 'usually at this stage they're still trying to figure out what they're going to do'. In my experience with friends, usually at this stage they figure out they're definitely screwed and start swearing like troopers.

tecmath: "life is fun."

me: "NO. NO ITS NOT."

WHAT IF WE HAVE TO START FIRST??

So you just have to make sure you leave an even number after you take your turn right?

I couldn't figure this out. No matter what I did, the computer (I ALWAYS made the computer move first) ALWAYS beat me. God ONLY knows what I was doing wrong.

This is frustrating me, I call B.S.on this method as you only show 1 game & it was totally confusing as to the "Person" taking the moves. I've played the Video through dozens of times & played the game but I just do NOT get the win. EVER.

Dumb. No explaination on screen. Missing annotations. This video is audio only. Disliked.

What if you have to start the game?

been playing this for half a century did not know its name we called it take a way and it was 1 2 3 4 5 in the 5 rows leave equals or 1 2 3 to win sometimes we added an extra row of 6

forgot also leave odd with 1 in each row

also forgot you can split the game into two sets like a even set and a 1-2-3 set

"Doesn't matter, too fun to watch"…😂😂😂

This doesn’t work if u have to go first?

You have the same strategy as Trevor Pasanen

I could beat you at nim but how would we play against each other

If the rule is that you can take the number of matches you want when it’s your turn, can’t you just take all the matches except one that you leave to your opponent?

So what’s gonna happen when two nim players collide in a battle? Doesn’t it make the winner a person who starts first? He just has to lead the game to the point where he’s leaving opponent with 6

I got to this video by watching Manhattan Murder Mystery by Woody Allen, when he’s talking to Diane Keaton about taking her to a film called Last year in Marienbad and in that film they played a game just like this.