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Puzzler against puzzler: A new way of playing.
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Author:  clm  [ Thu Oct 18, 2012 1:10 am ]
Post subject:  Puzzler against puzzler: A new way of playing.

Puzzler against puzzler: A new way of playing.

Do you know how to play Calcudoku, or better said, Min’s Calcudoku?. Like in chess the players make alternate movements. If I had to move first in the puzzle below I would place a 6 in a3 (I explain why below, in the Appendix). And after that a 2 in f4. Or, if this movemet is made by my opponent, I would place a 4 in f3.

This game could be used for “timed puzzles” so that the fast players could compete as commented long time ago by Patrick. But here the main idea is different since it’s more important to make “safe” movements, to think more, otherwise you quickly lose.

Here is the game I propose:

The game can be placed in “family mode” (or “stand alone”, with 2 or more players), with the players in front of the computer (of course any puzzler could train playing against oneself), or in “challenge mode” (only 2 players, both registered users) participating in different “coffe rooms” like in the site “”.

The rules:

A match consists of 5 games.

The puzzlers play alternately. Lots will be drawn to decide who moves first in the first game (modality “family mode”). In the following games the players rotate in the previously defined sequence. The players agree in: puzzle size, level of difficulty, “limit time” and cursor colour. These conditions are selectable in the page and maintained during the match (the number of players is selectable in the menu and the cursor colours are assigned to players 1, 2, 3, … , and 1, 2, 3 , … , also represent the sequence of play). Once a correct movement has been done the cursor goes to any available cell changing to the next colour (indicating the turn for the next player) and the clock restarts.

In the “challenge mode”, the “challenger” enters a “coffee room”, decides those parameters and moves first in the first game (and waits an opponent among the registered users in the site). The one accepting the challenge selects the own colour and can counterpropose once a different “limit time”, which could be accepted by the “challenger”.

A correct number in the cell is set to green colour and kept during the full game. An incorrect number is set to red and that player loses. If the time for the movement goes beyond the “limit time” stablished that player loses. In both cases the full solution is shown in background in the grid.

When a players loses, the winner (or winners if there are several players in the game) score 20 points. If the puzzle is completed to the end all players score 10 points. Apart of this, additional points are assigned to players in each game according, for instance, to the following table:

The total time of correct movements is calculated as a percentage of the maximum time possible for those movements (i.e., 8 correct movements, with a “limit time” of 4 minutes, represent a maximum time of 32 minutes):

Between 0% and 10% obtains 9 points
10% - 20% scores 8 points
20% - 30% scores 7 points
30% - 40% scores 6 points
40% - 50% scores 5 points
50% - 60% scores 4 points
60% - 70% scores 3 points
70% - 80% scores 2 points
80% - 90% scores 1 point
90% - 100% no additional points.

Comment: Probably the most popular could be a 5x5 standard, medium or difficult (with some single cell), with, let’s say, 1 minute of “limit time”. An 8x8 module function, for instance, could require 5 minutes per movement and could be indicated for very advanced players, the “skilled coffee room”.


For the puzzle below I estimate 4 minutes as an advisable time (mainly for the first movements). The initial calculations are in the graphic itself (the unicity of the solution require that cages "6+", in vertical and parallel, and cages "7+", in vertical and parallel, have different combinations; however, the same conclusion is obtained due to the puzzle structure, as explained in the text).


The numbers in green colour (encircled) indicate the movement number, in blue colour the first player movements and in brown colour the second player movements. This could have been a possible sequence:

The blue player moves a3 = 6, the brown player moves f4 = 2, the blue player moves f3 = 4 (a 4 cann’t be in b3 or c3 because it would produce a 3 in b2 or c2 but there is a 3 inside “8+” as we have seen above), the brown player moves a4 = 3 (a 3 is not possible in either “6+” cages and it’s not valid in b4 or c4 because it would generate a 4 in c4 or b4, respectively, but at least one of the two cages “6+” must be [2,4] as we have seen above), the blue player moves f2 = 6 (a 6 in b2 or c2 is not possible because it would produce a 1 in b3 or c3 against “3+”, and a 6 is not part of “8+”), the brown player moves a2 = 1 (a 1 in b2 or c2 would generate a 6 in b3 or c3 but there is already a 6 in row 3, in the cell a3), etc..

In this particular game moving first has not resulted in an advantage. Possibly the rest of moves would require much less time than 4 minutes but for the first movement 4 minutes is OK.

(Final comment: The real “challenge” now is to program all this :-) :-) ).

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