# 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:

- 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.
- 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.
- Diagonalize the resulting 18x18 matrix.
- Observe that the largest eigenvalue is 4913.
- 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**.

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*