When I present this material, I fill in the blanks during the course of the lecture (asking students for some of the answers).

Arithmancy 225 Halloween Puzzle

careful thinking useful not just for Computer Scientists  such as us
but also for 
as in ""
by :

[...]
    "Brilliant," said Hermione. "This isn't magic — it's logic — a puzzle. A lot of the greatest wizards haven't got an ounce of logic, they'd be stuck in here forever."
    "But so will we, won't we?"
    "Of course not," said Hermione. "Everything we need is here on this paper. Seven bottles: three are poison; two are wine; one will get us safely through the black fire, and one will get us back through the purple."
    "But how do we know which to drink?"
    "Give me a minute."
    Hermione read the paper several times. Then she walked up and down the line of bottles, muttering to herself and pointing at them. At last, she clapped her hands.
    "Got it," she said. "The ________ bottle will get us through the black fire — toward the Stone."
In-class Exercise (Participation):
During the remainder of this lecture,
write a careful solution of this puzzle
as follows:

  • Each of you work in a team of 2.

  • Use a sheet of ruled paper.

  • Write each of your names on the paper.

  • Each of you, if you have a nickname you want me to use when calling on you,
    write it on the paper.
    e.g. perhaps "Pat" if your full first name is "Patrick"
    e.g. perhaps "Alex" if your full first name is "Alexandra"

  • Write the following: 
        Problem:  7 bottles   __  __  __  __  __  __  __    by text preceding puzzle
                          b1  b2  b3  b4  b5  b6  b7
    need 7 labels:
    1 ahead (A) by line #3
    1 back (B) by line #4
    2 wine (W W) by line #5
    3 poison (P P P) by line #6
    (You each need to write this
    as you'll find sometimes clearly stating problem
    gets you halfway toward solution.)
    Note careful thinking/presentation includes justifications "by line ...".

  • Start writing inferences derived from the four clues.
    e.g. you should write the following: 
        inference #1:  by clue #2,
    I suggest that you skip clue #1 at first.

  • Continue writing inferences which you derive further.
    e.g. at some point you should write something like the following: 
        inference #4:  by inference #3 (clue #4) and the fact that
        there's more than one of only ,
  • Each time you determine the labels from some bottles,
    write the sequence of bottles showing which labels are determined
    and which are not
    e.g. as follows: 
            L1  L2          L3
    --  --  --  --  --  --  --
    b1  b2  b3  b4  b5  b6  b7
    Do not have only one bottle-sequence drawn on your paper
    with labels (gradually) filled in;
    if you were to do that, your progression toward solution would be unclear.
    In this course your careful thinking is evaluated;
    so you need to present such, clearly.