ITC Sudoku Mystery Cache

ITC Sudoku

This Sudoku (ITC_Sudoku.jpg) is, from a mathematical point of view, incomplete. To solve this Mystery you have to be skilled in solving Sudoku puzzles.

Start solving the ITC Sudoku (denoted T below and in Equation 1). Note that it is important to eliminate ALL impossible solutions (numbers) and no others. Once you have eliminated all impossible numbers you end up with a solution grid where some boxes have up to five possible solutions (numbers) if you are using traditional logic strategies. If you include extreme strategies you will have one box with four possible numbers and no one with five. The result will still be the same.

Once you have completed the task above you need to solve Equation 1 (Equation_1.jpg). This equation gives you the key (the correct number) for box 2B. Given this correct number, the ITC Sudoku becomes a mathematically correct Sudoku (denoted S), and you may continue eliminating all other impossible solutions and finally end up with only one correct solution for all boxes.

Equation 1 means that the correct number in position 2B (S_2B) is the sum of all correct solutions (numbers) in box T_8H minus the sum of all correct solutions in box T_1A minus the only possible solution in box T_5D minus the only possible solution in box T_5G.

To eliminate the last cheaters, a second equation has to be solved (and the correct Sudoku of course). Given the correct number, S_2B, it is possible to eliminate two numbers directly (one from box T_2C and one from T_7C) in the set of triplets {T_2C , T_6C , T_7C}. Those eliminated numbers are called e₁ and e₂ in Equation 2.

XXX= 56(e₁ + e₂) + 8                              Eq. 2

The final coordinates are given by:

N57°  48.XXX

E014°  1 (S_6B - S_6A) . S_1B (S_6A - S_1B) (S_6C - S_7B)