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This PG code shows how to include three different kinds of answer hints:

• General answer hints that help students get started on a problem and are always available via "Knowls".
• General answer hints that help students get started on a problem and are made available after a student has submitted an answer at least once (a "Show hints" checkbox appears near the "Submit Answers" button) via a `BEGIN_HINT / END_HINT` block of text.
• Specific, customized answer hints that appear in the answer feedback messages box after a student submits a particular answer that activates a pre-programmed hint via the `answerHints.pl` macro and a post-filter with answer hints for the answer checker.

You may also be interested in ErrorMessageCustomization

PG problem file Explanation
```DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
);

TEXT(beginproblem());
```

Initialization: We need to include the macros file `MathObjects.pl` and `answerHints.pl`, which only works with MathObjects answer checkers (not old answer checkers). General answer hints only require the standard macros, but specific (customized) answer hints require the `answerHints.pl` macro.

```Context("Numeric");
Context()->variables->are(t=>"Real",u=>"Real");

\$f = Formula("2 t");
```

Setup: We restrict the variables to `t` and `u`

```Context()->texStrings;
BEGIN_TEXT
If \( f(t) = \$f \), then \( f(3u) \) = \{ ans_rule(10) \}
\$BR
\$BR
\{
value=>'Substitute 3u wherever you see t in the formula for f.')
\}
END_TEXT

\$showHint = 5;
BEGIN_TEXT
\$PAR
If you don't get this in \$showHint tries, you can get a hint.
END_TEXT
BEGIN_HINT
Substitute \( 3u \) wherever you see \( t \) in the
formula for \( f(t) = \$f \).
END_HINT
Context()->normalStrings;
```

Main Text: Knowls (little bits of knowledge) provide an always present link to a hint that, when clicked on, expands to reveal the hint or, when clicked on again, retracts to hide the hint. The `value` of a knowl should be plain text (math mode may cause problems, as it did for me using ww 2.9). It is possible to get math to display, but it requires using a few escape tricks: `value=>escapeSolutionHTML(EV3P('Substitute \\(3u\\) ...')), base64=>1)`. In particular, note the use of `escapeSolutionHTML(EV3P())` to do extra interpretation of the string formatting and also note the use of double backslashes `\\( \\)` for the math mode delimiters. No special macros are needed for Knowls.

For hints that are revealed to students only after a certain number of submissions, we set `\$showHint = 5;` and tell the students in the problem text that they will see a hint after 5 attempts. We include a general answer hint in the block of text between the commands `BEGIN_HINT` (which is `HINT(EV3(<<'END_HINT'));` in older versions of WeBWorK) and `END_HINT`, which must be on their own lines and at the start of a line. The hint will automatically generate the word HINT: before the block of text that is the hint, so you don't need to add it manually. The modification of the context from `texStrings` and back to `normalStrings` ensures that MathObjects (formulas, etc.) will be beautifully typset. No special macros are needed for hints inside of `BEGIN_HINT` and `END_HINT` text blocks.

```\$showPartialCorrectAnswers = 1;

Formula("6 t") => "Are you using the correct variable?",
Formula("6 u") => "Good work!",
)));
```

Answer Evaluation: To generate specific, customized answer hints for particular answers, we use the `AnswerHints` postfilter provided by `answerHints.pl`. The answer hints should be provided by a particular answer, followed by the hash table association operator `=>`, followed by a string that will show up in the messages portion of the answer preview and feedback box when students submit their answers. You may include as many answer and hint pairs as you like, and even use subroutines in them (see answerHints.pl for more on this).

If the same error message should be given for several different answers, you should make a square bracketed list of those answers. For example, if the variables x, t, and u were all in the context, we could use

```ANS(\$answer->cmp()->withPostFilter(AnswerHints(
[Compute("6 t"),Compute("6 x")] =>
"Are you using the correct variable?",
)));
```

If the MathObjects answer evaluator normally generates a message, the default is not to change a message that is already in place. To override a message generated by a MathObjects answer evaluator, you should set `replaceMessage=>1` as below.

```ANS(\$answer->cmp()->withPostFilter(AnswerHints(
Compute("6 u") => ["Good work!",replaceMessage=>1],
)));
```