This FREE
Beta2.1 version is dedicated to all those supporting the struggle for a better future for this planet and its inhabitants wherever they are.
Numbers can be dragged and placed in the given formation or dragged back to get an equal sum for all shapes.
There is usually more then one arrangement that gives a right solution. You get a higher credit for each additional solution.

Soduko and KAMASUMA are LATIN games !!!

KAMASUMA and SUDOKU

KAMASUMA is the name of a large family of mathematical riddles, closely related to the family of LATIN games, of which the most familiar member is SUDOKU. In SUDOKU, the objective is to fill a 9×9 grid so that each column, each row, and each of nine 3×3 boxes contains the digits 1 to 9, once and only once. Note that if we add all the digits on each column, each row and each of the nine 3x3 boxes, we get an equal sum of 1+2+….+9=45.

In the following, we use the word pattern to designate a series of places which should be filled with numbers. The number of different number elements is equal to the number of sites or nodes of a pattern. The column, row and 3x3 boxes of SUDOKU, are each a pattern. In a LATIN arrangement each number element appears once and only once, in each pattern. Thus, SUDOKU is a LATIN game. In SUDOKU, under Latin arrangement, if we add all the elements on each pattern we get an equal sum, as mentioned above. Note, however, that we may get equal sum for each pattern even though the arrangement is a non-Latin arrangement.

KAMASUMA example

An example of a KAMASUMA game is shown in Figure 1. In the quatrogram of Fig. 1, there are only three different elements with a respective numerical value of 1, 2 and 3. The quatrogram has three triangular patterns, each with three sites. In the square grid of SUDOKU every pattern site is shared by three patterns, a column pattern, a row pattern and a 3x3box pattern. In contrast, in each triangular pattern of a quatrogram, two site are shared with the neighboring triangles, while one site is not associated with any other triangular pattern.

In the left quatrogram, the elements are arranged in a non-Latin arrangements. Yet, the sum of elements in each pattern is the same sum of five, as designated by the numbers inside the triangle. As a riddle, the player has to rearrange the elements so that an equal sum of six is obtained. The reader is advised to find a solution before continue to read the current article. As a hint we note that the desired arrangement is a Latin arrangement.


Fig. 1 A quatrogram KAMASUMA riddle with a solved non-Latin arrangement and a Latin arrangement

SUB-LATIN ARRANGEMENT

Finding a Latin arrangement may be facilitated by the concept of a sub-Latin arrangement. Suppose that one should place several elements of certain kind such that there is one and only one element of that certain kind in each triangular pattern. In the case of quatrogram, such a sub-Latin arrangement is possible with two, three or four elements. With two elements, for example the triple dot elements of Fig. 2, both elements are placed on two opposing shared sites. In the case of three elements, for example the single dot and the double dot elements of Fig 2, two elements are placed on non-shared sites of adjacent triangles, while the third element is placed on a site shared by the remaining two triangles. In a sub-Latin arrangement, four elements are placed on the four non-shared sites of the four triangles.

Fig. 2
Terms and Conditions  |  Priivacy Policy  |  Log In
Patent Pending      Copyright 2009 ©

Did you start playing and found the game to be too challenging? Do not give up! Click on the button






Once you press the "Get a Tip" button, you get two numbers within each triangle or square, a red number for the already accumulated sum   of entered numbers, and a green number for the expected equal total value.

 Rearrange numbers to have in red the same value as in green and the two numbers unite to a single number.  All done?   You win  !!!

You can also go to SETTINGS and change the level of the game difficulty

Remember, every combination you get has at least one solution. After getting a first solution, you are told how many additional and different solutions are there waiting for you.