How
to Write a Solution
Readers Are Not Interpreters
by
Richard Rusczyk
The first
thing a reader sees on your paper isn't the structure of your solution. It
isn't the answer, it isn't the words you choose. It's how the solution sits
on the paper. If the reader has to decipher scrawl, you're going to lose him.
Ideally, you'll typeset your solution with a program like LaTeX. However,
in most contests you don't have the luxury of turning to a computer and you'll
have to write it out by hand. There are few very important rules of thumb
when writing a solution by hand. Many are obvious, some are less so. You should
follow them all.
-
Use blank
paper. Don't use graph paper or lined paper - the lines often make solutions
harder to read. Never use paper that is torn out of a spiral notebook.
-
Respect
margins. If you are starting with a completely blank piece of paper, draw
the margins on all four sides (top, bottom, right, left). Make your margins
at least 0.5 inches, and preferably a full inch.
- Write horizontally; never
turn your writing when you reach the end of a line in order to jam in a little
more information. You can always start a new line or a new page.
- Leave space at the top
for a 'Page _ of _' so the reader knows how many pages there are, and what
page she's on. You probably won't know how many pages you'll write when you
start, but you can fill these out when you're finished. If you get to the
bottom of a page and your solution must continue on another page, write 'Continued'
at the bottom of that page so the reader knows we're not finished. (This also
helps readers know if they're missing pages.)
- Don't write in cursive.
Print. And print clearly.
- Use pen. If you must
use pencil, do not erase - the smudges from erasers make a mess.
- When you make a mistake
you'd like to omit, draw a single line through it and move on. If it's a large
block to omit, draw an 'X' through it and move on. Don't scribble out large
blocks of text.
- If you left something
out and want to add it at the end, put a simple symbol, like a (*), at the
point where you would like the new text to be considered added, and leave
a brief note, such as 'Proof below.' Below, you can write '(*) Addendum:'
and proceed with the proof. Don't use a bunch of arrows to direct the reader
all over the page.
Problem:
Let S(n) be the sum of the digits of n. Find
S(S(S(44444444))).
Below are
two solutions. Neither solution is picture-perfect; when you're under time
pressure, it's hard to write perfect-looking proofs. You should find the second
one much more enjoyable to read. When you're writing solutions, keep the above
tips in mind, and just remember, 'If they can't read it, it's not right.'
How
Not to Write the Solution:
That solution above
is a mess. The one below took me just as long to write, and is much easier
to read.
How
to Write the Solution:
