## MEAN SUMurai, a number game for sharp minds

For fans of all other kinds of logic puzzles

### MEAN SUMurai, a number game for sharp minds

Hi all
I'm not 100% positive that my game would qualify as a Sudoku variant but I'm pretty sure most sudoku players will find it interesting.
I just released it as an Android app with online multiplayer support. I've been playing/testing it
against friends and family but I got too good at it (I'm addicted and play the game about 2 hours a day). I need fresh blood.
Are you sharp enough to best me? Download the game, get good at it and challenge me for the top spot.

"Mean Sumurai is a unique maths game for sharp minds. You are given a number X plus
a sequence of digits and your task is to split the sequence to get numbers that add up to X.

For instance, with X = 81 and a sequence 15723, a winning splitting is 1 57 23 = 81.

Are you sharp enough to beat this game and its variants? Are you a number samurai?
Mean Maths

Posts: 5
Joined: 28 July 2013

### Re: MEAN SUMurai, a number game for sharp minds

Hi Mean Maths,
I'm 100% positive that this is not sudoku, therefore you posted it in the wrong forum.
Good luck
Tarek

tarek

Posts: 2908
Joined: 05 January 2006

### Re: MEAN SUMurai, a number game for sharp minds

Hi tarek

You are probably right. I think the forum "Other logic puzzles"
is a better fit. I would move the post there if I could.
May be I should create a new topic in that forum.

If you have an Android, please give the game a look.
[You can also use Blue Stacks on a PC or Mac]
It's free and you might like it. It is not Sudoku but it appeals to
similar logic.

Best,
Mean Maths

Posts: 5
Joined: 28 July 2013

### Re: MEAN SUMurai, a number game for sharp minds

If X were 204 and the sequence were 42162 then what would be the logical approach?
evert

Posts: 186
Joined: 26 August 2005

### Re: MEAN SUMurai, a number game for sharp minds

Hi Evert

"If X were 204 and the sequence were 42162 then what would be the logical approach?"

Similar to Sudoku, SUMurai is about enumerating possibilities and applying constraints.
Unlike Sudoku, it requires some basic addition skills. In many ways, it is easier than Sudoku
but can quickly confuse people: "Where do I start?"

Given your example, one can start by ruling out 421 as a possible split (bigger than X).
Therefore valid splits including 4 can only be 4 or 42. Here the example is not tricky enough
to justify going further than that. It would be overkill.
At this point, most humans can just see that the solution is 42 + 162.
In more complex examples, it is really a matter of being conscious about the constraints
that this or that split impose on the remaining sequence.

Let me highlight that, except for a very special case in the game, 3-digit splits are, for now, forbidden.
2-digit splits are more than enough to give interesting challenges.
See the examples below to be convinced of that.
They are random samples taken from the training page of the app (I was able to
solve them within a minute. They are not too hard but more than enough for a beginner.)

If you manage to solve them (which would be a feat, given that I just introduced the game to you)
you will get out of it with a more clear answer to your question
than all the babbling I did above

X = 77 for 15683
X = 79 for 532168
X = 88 for 191414941

Bonus: The MEAN version
Here, X is not the sum, but the mean of the splits. For example, with X=27 and 15723, the solution is 3 splits 1 57 23 which add up to 81; 81 / 3 = 27. So, you have to take into account the number of your splits. In fact, compared to the SUM version, this is where a big deal of logic come into play. In particular, you have to analyze the sequence to make an informed guess about which multiple of X you should go after.

X = 31 for 9579
X = 14 for 884653
X = 42 for 11398917

There are many more interesting variants in the game.
If you have an Android phone, just go and get the game. If not, install an emulator such as BlueStacks and play on your computer.

Best
Mean Maths

Posts: 5
Joined: 28 July 2013

### Re: MEAN SUMurai, a number game for sharp minds

Mean Maths wrote:In more complex examples, it is really a matter of being conscious about the constraints
that this or that split impose on the remaining sequence.

That would be obvious for all logical puzzles. If we were discussing sudoku you would probably agree that "... in more complex examples, it is really a matter of being conscious about the constraints
that this or that number impose on the remaining grid."
I like the puzzle concept but basically it's trial & error or chain reasoning - like searching for a mate in 4 combi.
evert

Posts: 186
Joined: 26 August 2005

### Re: MEAN SUMurai, a number game for sharp minds

Hi evert
I mostly agree with you but I really think you should download the game and go through its tutorial section.
It contains 5-6 lessons about the game variants and you will realize at the end of it that simple trial-and-errors
won't get anyone very far.
In particular, when some digits are hidden, you have to develop solid heuristics, though in some
cases you can also "cheat". Trust me, I struggled hard at the beginning but I can now "see" most answers for
medium difficulty instances. While playin, I developed some heuristics (that I won't share to anyone )
that are now literally running in background when I see a sequence.
I don't know if it is of any value in any context (may be for accountants ) but I can tell you that I improved a
lot on the type of basic maths skills required for this game.

If you doubt it, generate some reasonable instances (you just have to think about a set of numbers, glue them together and
give me X as their sum or mean) and challenge me with them. Of course, I have my limits and may fail but I would
enjoy such a challenge.
later
Mean Maths

Posts: 5
Joined: 28 July 2013

### Re: MEAN SUMurai, a number game for sharp minds

Looking at sums - not means:

You mentioned X = 88 for 191414941.

There are 4 solutions:

19-14-1-49-4-1
19-14-1-4-9-41
19-1-4-14-9-41
1-9-14-14-9-41

Were you aware of this?

How do you approach X = 994 for 815427436?
evert

Posts: 186
Joined: 26 August 2005

### Re: MEAN SUMurai, a number game for sharp minds

Sorry evert
evert wrote:Looking at sums - not means:

You mentioned X = 88 for 191414941.

There are 4 solutions:

19-14-1-49-4-1
19-14-1-4-9-41
19-1-4-14-9-41
1-9-14-14-9-41

Were you aware of this?

yup, there are often multiple solutions, even more so when some digits are duplicated.

evert wrote:How do you approach X = 994 for 815427436?

Normally, it is 2 digits at most but I can see that it is just impossible. So I guess you meant 3 digit splits.
...Live demo of how I approach it (may not be optimal, even by my own standards)
994
look for biggest 3-digit split
815 427436
815
look for next biggest split (allowing a sum below 994)
815 427436
... can already see that there is no way forward: the biggest compatible sum out of 427436 is 42+74+36=152 (+815=867<994)

Intuition tells me: try adding these 3-digit splits (because 5** + 4** likely 9**) 542 and 436 = 978
8 1 542 7 436
solution found

But I think the best demo for logical thinking is when there are hidden digits.
Consider this very simple example
27 for 2x78
If you consider the last 2 digits, you know you can't glue 7 and 8 for 78,
so you know 8 gotta be alone.
Then if you consider the first 2 digits, you know you can't glue 2 and the
hidden digit x because it would give 2x+8>27
So 2 gotta be alone.
So here you have 2+8=10 and x7
so you know x gotta be 1 for 2+8+17=27.

This is really a toy example but in many cases, you really need elaborate thinking
(set up combinations that would work if digit has a certain value) to guess which digit is hidden.

If you have an Android (I'm working on an iOS version), you should really try the game.
I recently added an Arena mode
where people can download games solved by other players and try to do better.

Best
Mean Maths

Posts: 5
Joined: 28 July 2013