Thought the same, you beat me to it! Really like the tree-like view, might steal that idea later :-)

https://bewelge.github.io/aNumberGame/ (does not format well on mobile)

Code: https://github.com/Bewelge/aNumberGame

I like that all possible moves are shown at once. Would it be possible to have the sequence be other than [7, 5, 3]?

I added an url parameter so you can load it up with any sequence.

Example for sequence 5,2,7

https://bewelge.github.io/aNumberGame?seq=5,2,7

Thanks!

Fun implementation! There's currently a bug that allows the same number to appear twice after a combination step (I was able to perform 2,3,7,5->5,7,5)

Ran into this as well: I did [8, 1, 4] -> [5, 3, 1, 4] -> [5, 3, 5].

Should be fixed, thanks for the report.

Jumping in with my janky version: http://poyo.co/list-of-integers/

I really like the visual aspect of your implementation

This is neat, but your implementation does seem to allow duplicates sometimes

Should be fixed now, sorry for trouble.

Interesting, it appears I've encountered an impossible combination of numbers: [2, 5, 1, 3]

The only possible move is to add 1 and 3. Can't ever split a 2 as that would result in [1, 1], can't split the 5 because that would be [4, 1] or [3, 2], can't split the 3, as that would be [2, 1] or [1, 2], can't add the 5 to anything as that would be larger than 5.

Couldn't you split 3 into [4,-1] ?

None of the implementations support negative numbers, but the rules say integer which includes negative numbers, so that should be a legal move.

They also say that a given integer should be split into two smaller integers.

Negative numbers would break the game by making the number of possible splits infinite. E.g. 1 could split into [-2, 3], [-3, 4], [-4, 5], etc.

It also violates Rule 1 because one of the splits is larger than the original number.

Rules say you can’t ever produce a number greater than the original largest number, so the possibilities will always be finite. (fixed number of ways to make a list of distinct integers that sum to N such that all values are <=M).

You're right in the first sentence, but you're second sentence if we're talking about splitting the largest original number itself that way.

I was given [1,2] in the second run. Even easier to see it's impossible.

Yeah the generation is very simple, 2-4 random numbers between 1 and 9 inclusive. Definitely gives impossible puzzles sometimes (because I don't know a general algorithm for generating possible ones only).

If you only have numbers up to 9 an exhaustive search shouldn't be too bad (should be ~9! states if you memoize), you could implement a solver in Javascript and see whether a solution can be found before you give it to the user.

Gave me [2,1] which is not possible

It does seem like [n,n+1] is always unsolvable!

[9,8] -> [6,3,8] -> [6,2,1,8] -> [6,2,9] -> [8,9]

Indeed,

   [n, n-1] 
   [n-3, 3, n-1]
   [n-3, 2, 1, n-1]
   [n-3, 2, n]
   [n-1, n]

Works for all n greater than... 6?

Optimizing self-response! That fails for six because n-3 and 3 co-occur. With a slight modification we can make it work for all n>5

  [n, n-1]
  [2, n-2, n-1]
  [2, n-3, 1, n-1]
  [2, n-3, n]
  [n-1, n]

edit: and it's not hard to show that n<6 are impossible, so the solution above is optimal in that sense.

Yeah, the [n,n+1] is only a problem when there isn't enough wiggle room between the numbers. ex: [2,3] and [3,4]

[3,4]

--> [1,2,4] --> 4 can't split because 2/2 and 3/1 are invalid

--> 4 can't initially split because 2/2 and 3/1 are both invalid

[5,6] --> [5,4,2] --> [5,1,3,2] --> [6,3,2] --> [6,5]

[7,8] --> [7,3,5] --> [7,1,2,5] --> [8,2,5] --> [8,7]

When you add more numbers, you need more wiggle room. So, [4,5,6] is problematic and probably [5,6,7].

[4,5,6]

--> [3,1,5,6] --> 6 can't break into 3, nor 5/1. It can do 4/2, but then 5 can't split. 5 also can't split.

--> [4,2,3,6] --> [4,2,3,1,5] --> [6,4,5] --> 4 can't split into 2/2. It can split to 3/1 but then 5 can't split

--> 6 can't initially split at all because 3/3, 4/2, and 5/1 are invalid

Even if [6,7,8] has a solution, I'm sure [6,7,8,9] does not.

A solution for [6,7,8,9]:

6,7,8,9

6,3,4,8,9

6,3,4,8,2,7

9,4,8,2,7

9,4,8,2,1,6

9,4,3,5,2,1,6

9,7,5,2,1,6

9,7,5,3,6

9,7,8,6

9,5,2,8,6

9,5,2,1,7,6

9,5,3,7,6

9,8,7,6

Wow, well done! I found [6,7,8] as well:

6,7,8

6,7,5,3

6,7,1,4,3

6,8,4,3

6,8,7

6,3,5,7

6,2,1,5,7

8,1,5,7

8,6,7

8,4,2,1,6

8,4,3,6

8,7,6

Would be nice if you allowed users to define their own puzzle. I had to set a break point at the right location and call startNew([..my array]) to do so.

Added, you can use ?numbers=1~2~3 to specify your puzzle.

Like this:

https://blaise.gg/number_game/index.html?numbers=1%7E4%7E6%7...

Nice. It does let me make the same integer twice though.

Should be fixed now, sorry for trouble.

I think it would be more fun if you only displayed problems that are solvable.

Yeah, I would but finding such puzzles is kind of hard. Might look into it this weekend

I'm sure we could write a brute force tester, and then you would only have to include a list in your webapp. Or harvest people's results

Cool!

Though I say the rule about repeated numbers is a bummer. I can see things might get easier (also it might be a more procedurally easy problem to solve) if this is allowed

Basically I don't think it's a "productive" complication

Without that rule, you could decompose everything into 1's, and then recompose from there. Not the most efficient solution, but a boring one that always exists.

Ok so how about allowing only non contiguous repeated numbers