Re: Christmas Calcudoku 2012-2013

nicow wrote:

I have to admit, that I do not understand how -2, +2 and x2 could be a 'linear combination'...?

Thanks for your interest and comment, initially I have intentionally left the things a little "dark" in order to make attractive the clarification of what's that of "linear combination".

The operation itself is a subtraction "-", an addition "+" and a product "x"; for instance, in the cage "48x2", 48 is the final result, the operation is a multiplication, and the final 2 means that the

**rest** of the operands are multiplied by 2, in this particular case (two cells) there is only one operand affected, that is, a x (2b), so 4 and 6 are the operands, or in other words [4,6] is the only valid combination since 4 x (2x6) or 6 x (2x4) produces 48 in both cases.

Now, let's suppose we had the result "11+2" (two cells), we would have these possibilities: [1,5], [1,9], [2,7], [3,4], [3,5], that is, one of the numbers plus twice the other number sums 11. We could say that the operation a + 2b is a linear combination.

A cage "1-2", in three cells, can be obtained with [1,1,5] since 5 - 2x1 - 2x1 = 1.

Finally, if we had "27+3" in a 7x7 Calcudoku (in the proposed puzzle there are not cages with a 3 after the operator), in three cells, what we propose is: a + 3b + 3c, so for instance [1,3,7] is a solution since 3 + 3x1 + 3x7 = 27, but another solution, for instance, could be [3,4,6] since 6 + 3x3 + 3x4 = 27, etc.