Logic Masters Deutschland e.V.

Tantalizing Sandwiches

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Sudoku	Fill the grid with the digits 1-9 so that no row/column/3x3box contains repeated digits.
Tantalus	(always out of reach) A clue (X) outside the grid indicates that in the corresponding row/column/diagonal the digit X may not appear in the first X cells away from the clue.
Sandwich	A clue (X) outside the grid indicates the sum of the digits sandwiched between a 1 and a 9 in the corresponding row/column/diagonal.
	Digits may repeat on diagonals. In case of multiple sandwiches along the same diagonal, only the widest sandwich counts, i.e., the sandwich between the 1 and the 9 that are the farthest apart.
Find <T>	The digit T must be determined by the solver.
Kropki	Cells separated by a white dot contain consecutive digits. Not all dots are given (i.e., there are no negative constraints).

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Inspired by the Tantalus rules from PjotrV's Torment of Tantalus

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Fun fact: I created this puzzle entirely without using any automated solving tools. I usually rely on such a tool to quickly gauge whether one or more solutions exist. This puzzle however was set by manually trying to solve it for each clue that was added/removed/changed, until I was satisfied with the result, which was this very puzzle.