My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Reply
 
LinkBack Thread Tools Display Modes
June 6th, 2018, 11:58 AM   #1
Newbie
 
Joined: Feb 2018
From: California

Posts: 17
Thanks: 1

Addition Nim

I am unfamiliar with the game of Nim and I am just learning that there are MANY different versions out there.

I want to learn about Addition Nim, where two players count to a number (n) and the winner says n at the end.

For example, the first person to say "20" wins. Rules are that you can add either 1, 2, 3, or 4 on your turn, but you must add something. The first person must start at 0. So it can progress like:

1st person: 0
2nd person: 1, 2, 3, or 4
1st person: 5
2nd person: 6, 7, 8, or 9
1st person: 10
2nd person: 11, 12, 13, or 14
1st person: 15
2nd person: 16, 17, 18, 19
1st person wins with 20

For this example, I see how to win. You should pick multiples of 5 so that your opponent can never quite reach 20. (Or is this not accurate? That's what I came up with.)

I want to know how to figure out strategies for other examples, too. For example:

1) if the goal is 20 and you can only add 1 or 2. How does the strategy change? I can see that you want to have 17 as your last number, but how do I guarantee that throughout the game?

2) if the goal is 21 or 22 and you an add 1 through 4, what is the strategy?

3) if the goal is 21 or 22 and you can add 1 or 2, what is the strategy?

Is there an overall strategy that applies to all Addition Nim games like these?
mjsilverfly is offline  
 
June 6th, 2018, 12:24 PM   #2
Newbie
 
Joined: Feb 2018
From: California

Posts: 17
Thanks: 1

Actually, I think I have something. Correct me if I'm mistaken....

does it have to do with mod math? So if let's say the goal is to say 22 and you can only count by 1, 2, 3, or 4, you need to always say a number with remainder 2 when you divide it by 5, so you'd have to say 7, 12, then 17, then win.

So you divide by 5 in this example because you can only count up to 4. Does this make sense?
mjsilverfly is offline  
June 7th, 2018, 12:27 AM   #3
Senior Member
 
Joined: Apr 2014
From: UK

Posts: 892
Thanks: 328

It looks like you've solved it to me. You could formalise this:
n= final target
m= maximum increment allowed (4 in the example)
r= remainder of n / (m + 1)
x= any number (will want to start at 0 or 1 and increment by 1 on your turn until the target is reached)

step targets are then (m+1)x + r

If r is 0 then the first player (who starts at 0) wins, otherwise the second player wins.
weirddave is offline  
June 7th, 2018, 01:06 PM   #4
Newbie
 
Joined: Feb 2018
From: California

Posts: 17
Thanks: 1

Awesome! Thank you!
mjsilverfly is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
addition, nim



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
[ASK] Fraction Addition Monox D. I-Fly Elementary Math 3 May 14th, 2018 11:48 PM
Addition krishanu05 Math 1 June 26th, 2014 11:15 AM
addition algorithm gelatine1 Computer Science 1 April 29th, 2014 01:44 PM
What's between addition and division? 1Reebok Elementary Math 5 October 9th, 2012 06:01 PM
addition is well-defined tinynerdi Real Analysis 5 January 10th, 2011 12:51 PM





Copyright © 2018 My Math Forum. All rights reserved.