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copied!<p>I don't understand clearly this part about rotations but for this scenario:</p> <p>There are 3x3=9 holes and 10 cases and every time only one case can take place:</p> <pre><code>Case 1 = no holes Case 2 = one hole ... Case 10 = 9 holes </code></pre> <p>Then it would go like this with the combination formula C(n,k):</p> <blockquote> <p>Total = C(9,0)+C(9,1)+....+C(9,9)</p> </blockquote> <p>this is to sum k different combinations of n elements.</p> <blockquote> <p>Totol = 1+9+36+84+126+126+84+36+9+1 = 512</p> </blockquote> <p>I think you are right, 512 seems to be correct and theoritically pinless is defined as a combination too, if you don't want it just remove it to get 511.</p> <p>All these cases happen separately so we add the different cases.</p> <p>If they were to happen synchronously, for example calculating the combinations for 3 employees punching the paper once or calculating the combinations for marking the paper 3 times by one employee then it gets more complicated and should be 512 * 512 * 512 by the nxm rule.</p> <p>The m*n rule in a simple display is:</p> <p>I have 4=m pockets and two=n hands:</p> <blockquote> <p>my_left * 4(pockets)=4 my_right * 4(pockets)=4</p> <p>total= 4+4=4*2=m*n</p> </blockquote> <p>Only one hand can enter the pocket at a time or only one combination of one employe is paired with only one combination of the other employee and this is the exact reason we take the m*n rule. </p> <p>This is what I think, I am not a mathematician and do not claim to be correct 100%, it's just what I remember from the probabilities course. </p> <p>I don't claim to be 100% correct, is jus what I remember for the probability course.</p> <hr> <p>As for patterns overlapping, checking if pattern already found etc I wouldn't bother at all since there are so many algorithms in pseudocode that generate combinations. Since they generate then no need to check overlaps or anything. </p> <p>After all this is what generat means it is designed a priori to find all results, just let it run.</p> <p>I had found once a even more rare algorithm than simple combinations and when I turned it to php it did the job perfectly, no need to worry for overlaps or anything. </p>

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