# Annotated Solution to the Jotto Puzzle of the Day

## May 5, 2003

NOTE: This puzzle actually has more than one solution. I believe this
happened because I generated it when my dictionary was smaller. Thanks to
the person who spotted this and pointed it out to me. Needless ot say,
this won't happen again.

canto - 1
built - 2
foist - 2
admit - 2
cedis - 1
inept - 2
stale - 2

No zeros here, so we're in for some work.
Might as well start at the top. If there's a **c**, then there's no
**a**, **n**, **t**, or **o** (canto=1). Working our way down
the list, we see that we must have two of **d**, **m**, and **i**
(admit=2 and anto=0). However, since there is a **c**, we know there is
no **e**, **d**, **i**, or **s** (cedis=1). That means it's
impossible to have two of **d**, **m**, and **i**, so we have a
contradiction. Therefore, there is no **c**.

Let's try the next letter in **canto**. If there's an **a**, then
there's no **c**, **n**, **t**, or **o** (canto=1). Looking at
**built**, we know that we must have two of **b**, **u**,
**i**, or **l**. Working our way down the rest of the list in a
similar fashion, we have the following:

a(buil=2)(fis=2)(dmi=1)(edis=1)(iep=2)(sle)

That doesn't look too helpful at first, but we can break it up into smaller
units. Starting from the left, we see that there are 6 combinations from
(buil=2), which is a lot. However, there are only 3 combinations from
(fis=2), so let's look at that.
If it's **fi**, then, knocking out **i** from some of the
combinations, we have:

a(bul=1)fi(dm=0)(eds=0)(ep=1)(sle=1)

Taking the new zeros into account, we can reduce (ep=1) to **p**, and we
can reduce (sle=1) to **l**. This gives us the five letters
**afipl**. Since we're left with exactly five letters, this looks like a
good opportunity to see if we can make a word out of this. Some playing
around with ordering of the letters turns up the solution, **pilaf**.
Since we've found a word, we know we can stop because this is a Jotto
puzzle, which by definition only has one word that works.

kevin@aq.org

Jotto Puzzle of the Day

Jotto

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Last modified: 06 May 2003