`````` ###########################################################
#    If the final answer is correct, then the problem is given full credit
#    and a message is generated to that effect.  Otherwise, partial credit
#    is given for previous parts.``````

`````` ################################################################
#
# We need a special problem grader on this problem, since we
# want the student to get full credit for all five answers correct,
# 60% credit for four correct, and 0% for three or fewer correct.
# To change this scheme, look through the following mess of code
# for the place where the variable \$numright appears, and change
# that part.
# Also change the long line beginning "msg ==>", to show what will
# appear on the screen for the student.
#
# To look at the problem itself, look for the boxed comment below
# announcing the problem itself.
################################################################``````

### NOTE:

`````` ################################################################
# was contributed by Prof. Zig Fiedorowicz,
# Dept. of Mathematics, Ohio State University on 8/25/01.
# As written, the problem grader should be put in a separate macro file.
# If actually inserted into a problem, you need to replace a couple
# of backslashes by double tildes.
#
# This is a generalization of the previous custom grader.
# This grader expects two array references to be passed to it, eg.
# Both arrays should be of the same length, and in strictly
# increasing order. The first array is an array of possible
# raw scores, the number of parts of the problem the student might
# get right. The second array is the corresponding array of scores
# the student would be credited with for getting that many parts
# right. The scores should be real numbers between 0 and 1.
# The last element of the 'grader_scores' array should be 1 (perfect
# score). The corresponding last element of 'grader_numright' would
# be the total number of parts of the problem the student would have
# to get right for a perfect score. Normally this would be the total
# number of parts to the problem. In the example shown above, the
# student would get 10% credit for getting 2-4 parts right, 40%
# credit for getting 5-6 parts right, 60% credit for getting 7-9 parts
# right, and 100% credit for getting 10 (or more) parts right.
# A message to be displayed to the student about the grading policy
# for the problems should be passed via