Law of Induction
(Published on 6. November 2025, 18:10 by Tobias Brixner)
Puzzle link: Play on SudokuPad.
Rules: Normal Sudoku rules apply.
A black line surrounding one or several cells represents an open electric wire loop that moves along the direction of the attached black arrow with a constant velocity of one cell at a time and with constant shape. Digits encompassed by the loop on its path constitute magnetic fields. The magnetic flux through the loop is the sum of the magnetic fields it contains at each position. The loop movement leads to a varying voltage; for each step, it is equal to the magnetic flux difference between two adjacent loop positions.
The absolute magnitudes of voltages are recorded in adjacent cells along a red line. The first record for each loop occurs in the cell whose red letter (A-G) in the top right corner is the same as the black letter in the top left corner of the loop. That starting value corresponds to the absolute magnitude of the voltage when the loop moves from its initial to the adjacent position one cell further in arrow direction. Subsequent steps are recorded in the direction of the red arrow. When the red line ends, any further voltages of that loop are no longer recorded.
Your feedback, ratings and comments are highly appreciated. Have fun!
Background: This puzzle incorporates the correct physical equation of Faraday's law of induction that describes how a changing magnetic flux induces an open-circuit voltage. How a voltage leads to a current in a closed circuit is described in my puzzle Electric Circuits.
Acknowledgment: The inspiration for this puzzle came from an idea of user PiCube (CTC Community on Discord) who asked if it was possible to construct a Sudoku with a wire loop moving across magnetic fields. Instead of plotting the resulting voltage curve graphically outside, in the current puzzle the voltages are recorded as numbers in the grid itself on the red lines (think of them as graph plotters).
Example: The following image provides a fully solved example on a 4x4 grid. You may solve the example for yourself here on SudokuPad.
Solution code: All digits of column 8 (from top to bottom) without spaces.
Comments
on 6. November 2025, 23:08 by dzamie
So, to make sure I understand how the example works (i.e. why it's correct):
Step 0: loop contains digits summing to 7
Step 1: loop moves right, new digits sum to 3, for a difference of 4 with past step
Step 2: loop moves right, new digits sum to 4, for a difference of 1 with past step
Step 3: loop moves right, new digits sum to 6, for a difference of 2 with past step
4, 1, 2 are recorded on the red line in the order of the red arrow.
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Yes! - TB
