It has been a long time since I wrote a variation on TomTom, which is a less constrained version of KenKen. The last time, it was about having cages with operations alone as givens, instead of numbers and/or operations. I gave it a peculiar title "Operator magic".

This new variant retains the usual flavor of givens as numbers and/or operators, but there is a twist. A set of digits is provided alongside the grid. This set is found in every cage that involves a particular operation, while it is ok if the set is also found sporadically in some of the other cages as well. On to the rules:

Insert a digit from 1 to N into each cell of the NxN grid, so that no digit repeats in any row or column. The clue in each outlined cage indicates the result of a mathematical operation applied successively to each of the digits in the cage, starting from the largest to the smallest for division and subtraction. The operation may or may not be given in the cage, but at least one of the four operations must apply. Digits can repeat within a cage. A set of digits is given along with the puzzle. This set must be found in every cage that involves a particular operation. This operation is not given and has to be determined during the solve.