Logic Masters Deutschland e.V.

Click on the puzzle image to play! Solve the 4x4 first if you desire additional help (see explanation below).

You are a scientist working in a research institute. Unfortunately, there was an explosion and radioactive radiation sources were scattered throughout your lab. Find your path to the exit and monitor your radiation dose...

Rules: Normal Sudoku rules apply.

Cells with radioactivity symbols are radiation sources and contain the digits 1 to 9 once each signifying their “radiant flux” Φ.

Each radiation source causes an “irradiance” E in other cells, obtained as the radiant flux Φ divided by the square of the considered cell's distance r from the source, the result of which is rounded down to the nearest integer, i.e., E = ⌊Φ/r²⌋ using the “floor operator” ⌊ ⌋ to denote rounding down. Distance is measured in units of cells between cell centers. For a horizontal separation x and a vertical separation y, the distance r is calculated using the Pythagorean theorem (r² = x² + y²).

The total irradiance in a cell is the sum of irradiances from all radiation sources.

Draw an orthogonally connected, unbranching path from the scientist to the exit without entering cells that contain radiation sources. Each cell on the path, including the initial and the final cell, must contain its total irradiance as a digit.

The dosimeter must contain the sum of all irradiances on the path as a two-digit number with the tens on the left and the ones on the right.

Given digits are on the path.

This puzzle took a very long time to set. Please leave a comment if you like it!

Reveal calculated E = ⌊Φ/r²⌋ patterns as a solution aid: If you solve the 4x4 example below, it might give you a better feeling for the puzzle mechanic. Click on the puzzle image to play. As a bonus, you may then enter the digits of column 3 here to reveal the irradiance patterns. This could ease the solution of the 9x9 version. The patterns are displayed independently of the puzzle grid so that the solution path is not spoiled strongly. This allows you to double-check your calculations of E.

Background: The puzzle rules incorporate the physically correct inverse-square law of point emitters. Because of the rounding down, obtained irradiance values are lower bounds. The named quantities correspond to the recommendations in radiometry. We ignore a suitable proportionality factor because we can assume this to be part of the physical unit for Φ.