# Numberless Sudoku with Just a Letter and Symbol Combination

A Standard 9x9 Sudoku uses the digits 1 to 9.

You are only allowed to use a single letter(say T) and a symbol of your choice to represent the digits 1 to 9.

Rules should be well defined and the combination should be aesthetic and have minimal footprint.

Find out the minimum number of characters (letter-symbol combination) needed to construct a Sudoku puzzle with a unique solution.

Advantage of this compared to previous puzzle based on 2 primes is the playability based on pattern alone if needed.

• What do you mean by "Rules should be well defined and the combination should be aesthetic and have minimal footprint."? How exactly do you want the digits to be represented? – Deusovi May 28 at 16:31
• The puzzle is causing confusion.. I would answer it myself. And thus avoid any further misinterpretation. – Uvc May 28 at 17:21
• If my explanation is not satisfactory, you can delete or put on hold. – Uvc May 28 at 18:02
• why can't you just have I = 1 and then say something like put a dot on the top its *2, top-left is *3, etc. It seems way too arbitrary and the one with the most "aesthetic and have minimal footprint" seems way too subjective. IMO this isn't really a puzzle... – ev3commander May 29 at 4:01
• Sure..you can have any system you desire...T signifies 2...rest of the numbers are built around by assigning various arithmetic operations to the position of the dot..main intent of the puzzle was to design a visual pattern based system ..yet retaining the number based feature of sudoku...as far as I know this kind of sudoku is not there...by downvoting people have expressed their opinion and it is ok with me..sometimes radical concepts are hard to accept initially till it becomes mainstream. – Uvc May 29 at 8:40

I don't think this is much of an answer because I don't think I've added anything new.

In order for the puzzle to be playable, we would need to have all 9 digits representable in our customisation.

So for the symbol, I will use + and for the character T. Here is one way to encode 9 distinct sets using 'T' and '+'.

T      +     TT
++     T+    +T
TTT    +++   T+T

Now, using the minimal configuration we have a distribution of symbols (1,3,4,2,1,2,0,2,2). Use the following assignments:

1. TTT
2. +
3. T
4. TT
5. +++
6. ++
7. T+T
8. T+
9. +T

This gives us $$21$$ symbols in the puzzle for that configuration.

• Both letter and symbol need to be there in representation of each digit..proper symmetry can be maintained for easy play based on visual pattern – Uvc May 28 at 15:00

Intent of the puzzle is to create numberless sudoku system which can represent all the digits as well as a pattern which could be used to solve sudoku.

My intent was not properly conveyed.

Here is my thinking:

Letter “ T “ represents number 2. Symbol I select is dot “.” Based on defined rules, all other numbers are generated to be used in Sudoku representation.

Dot on top right like exponent..represents ten compliment. Bottom right represents square..

$$T$$...$$2$$. $$T^.$$...Repesents compliment.... $$8$$

$$T.$$ 2x2=4

Once we define all other numbers with proper combination of “dot” with T and applying the above rules, all digits can be represented.

Will summarize first and then show the representation for all numbers.

Dot on top left..1. Dot on bottom left....3

Dot on bottom right ..square the number..$$T.$$ is 4

$$^.T$$ 1

$$T$$ 2
$$T^.$$ 8

$$.T$$ 3 $$.T^.$$ 7

$$T.$$ 4
$$T^.$$. 6

$$T$$ 5 Dot under T signifies 5 .

Because of my poor formatting skills, I might not have presented properly.

In essence, Location of Dots changes the value T=2 to

All other digits to be used in soduku. If we format the dot properly, lt should be visible better.