Solution to Disarray

by Andrew Thomas

The first part of this puzzle is a standard diagramless crossword. Ignore the "leftovers" for now; save them for later.

Note that the To find clues give An integral eigenvector of the largest real eigenvalue. So:

  1. Convert the grid letters to numbers via A=1, B=2, etc. This is suggested by the answers to 9 down and 90 across, which indicate that this puzzle is like AONE and BTWO.
  2. Enter the leftovers in the leftover (black) squares. As a hint for this step, converting the small integers in the leftovers back to letters spells ENTER THE LEFTOVERS INTO BLACK SQUARES IN THE USUAL ORDER.
  3. Diagonalize the resulting 18x18 matrix.
  4. Observe that the largest eigenvalue is 4913.
  5. Normalize the corresponding eigenvector so that its smallest element is 1, and look at the result.

You should get something very close to the column vector

[25 15 21 18 1 14 19 23 5 18 9 19 6 18 9 5 14 4]

Converting this back to letters gives YOUR ANSWER IS FRIEND.

disarray.png

Solution fixed in 2010 by the archivists of Beginner's Luck. Originally the eigenvector had an additional number 13 before the 6, and showed this grid from a different version of the puzzle.

2006 MIT Mystery Hunt