Advisor's Nightmare: Solution

By Dan Katz

Answer: PREREQUISITE

In catalog order, the Disclaimer Codes spell “COURSE TITLES CAN BE IGNORED WHEN SOLVING.” Indeed they can be.

There is a unique way to schedule all of the courses (including ENGM 145 twice) to satisfy the given constraints. One possible logical path to the solution is given at the bottom of this page.

TypNum stands for Typical Enrollment Renewal Number After Registration Year, which could also be abbreviated as TERNARY. For each semester, the TypNums of the three courses can be read, ordered by course time, as a three-digit ternary (base three) number. These numbers can then be converted to letters (A=1, B=2, etc.) to form the phrase COURSE MOD SIX.

If the course numbers are reduced modulo six (that is, replaced with their remainder after dividing by six), the results are all 0's, 1's, or 2's. Reading these numbers as base three digits again (in the same order) gives the phrase TS IN PROF NAME. Each course professor's name has 0, 1, or 2 T's in it, and when these digits are read one more time as base three digits, it results in the answer to the puzzle, PREREQUISITE.

Semester	Year	Time	Course	TypNum		Course Mod 6		T's in Prof
Fall	2017	1pm	ENGM 332	0	C	2	T	1	P
Fall	2017	3pm	ENGM 402	1	.	0	.	2	.
Fall	2017	4pm	ENGM 308	0	.	2	.	1	.
Winter	2017–2018	1pm	ENGM 440	1	O	2	S	2	R
Winter	2017–2018	2pm	ENGM 390	2	.	0	.	0	.
Winter	2017–2018	5pm	ENGM 373	0	.	1	.	0	.
Spring	2018	3pm	ENGM 289	2	U	1	I	0	E
Spring	2018	4pm	ENGM 516	1	.	0	.	1	.
Spring	2018	5pm	ENGM 438	0	.	0	.	2	.
Fall	2018	1pm	ENGM 397	2	R	1	N	2	R
Fall	2018	3pm	ENGM 421	0	.	1	.	0	.
Fall	2018	5pm	ENGM 176	0	.	2	.	0	.
Winter	2018–2019	2pm	ENGM 205	2	S	1	P	0	E
Winter	2018–2019	3pm	ENGM 128	0	.	2	.	1	.
Winter	2018–2019	4pm	ENGM 145	1	.	1	.	2	.
Spring	2019	1pm	ENGM 512	0	E	2	R	1	Q
Spring	2019	2pm	ENGM 234	1	.	0	.	2	.
Spring	2019	4pm	ENGM 426	2	.	0	.	2	.
Fall	2019	1pm	ENGM 145	1	M	1	O	2	U
Fall	2019	3pm	ENGM 272	1	.	2	.	1	.
Fall	2019	5pm	ENGM 156	1	.	0	.	0	.
Winter	2019–2020	2pm	ENGM 468	1	O	0	F	1	I
Winter	2019–2020	4pm	ENGM 344	2	.	2	.	0	.
Winter	2019–2020	5pm	ENGM 180	0	.	0	.	0	.
Spring	2020	3pm	ENGM 115	0	D	1	N	2	S
Spring	2020	4pm	ENGM 475	1	.	1	.	0	.
Spring	2020	5pm	ENGM 530	1	.	2	.	1	.
Fall	2020	1pm	ENGM 474	2	S	0	A	1	I
Fall	2020	3pm	ENGM 102	0	.	0	.	0	.
Fall	2020	5pm	ENGM 199	1	.	1	.	0	.
Winter	2020–2021	1pm	ENGM 361	1	I	1	M	2	T
Winter	2020–2021	2pm	ENGM 253	0	.	1	.	0	.
Winter	2020–2021	5pm	ENGM 265	0	.	1	.	2	.
Spring	2021	1pm	ENGM 504	2	X	0	E	0	E
Spring	2021	3pm	ENGM 343	2	.	1	.	1	.
Spring	2021	4pm	ENGM 428	0	.	2	.	2	.

Here's one way to logically reconstruct the course schedule:

516, 397, 145 (the first time), 145 (the second time), 344, 199, and 343 must be taken in that order. Because of the semesters they are available, 516 must be taken in S18, 397 in F18, 145 in W18–19 and F19, 344 in W19–20, 199 in F20, and 343 in S21.

504, 512, and 530 are only offered in the Spring and can only be taken one a time, so they are taken in S19, S20, and S21 in some order. 512 must be taken before 272, and 272 conflicts with 199 in F20, so 512 is taken in S19 and 272 in F19. 253 must be taken in the Winter after 530, so 530 is taken in S20, 253 in W20–21, and 504 in S21.

390 and 373 must be taken in the same trimester, at least nine trimesters before 361. 373 cannot be taken F17, and 361 conflicts with 504 in S21, so 390 and 373 must be taken in W17–18 and 361 in W20–21.

128 and 205 must be taken in the same trimester which can’t be Fall or Spring, so it must be Winter. Only W18–19 and W19–20 have room for two more classes, and 128 conflicts with 344 in W19–20, so 128 and 205 must be taken in W18–19. 156 must be taken the trimester before or after 512, and since W18–19 is now full, 156 must be taken in F19.

102 must be taken in a trimester that is consecutive with the trimesters of both 115 and 265 (which must be different). Since there is no trimester before F17, the trimester after F18 is full, and F19 is full, 102 must be taken in F20. 265 conflicts with 530 in S20, so 115 must be taken in S20 and 265 in W20–21.

The nine Sudoku Seminars must be taken in different trimesters, and since W18–19, F19, and W20–21 are now full, the Sudoku Seminars must be taken in the other nine trimesters. 308 and 332 must be taken in the same trimester, and taking the Sudoku slot into account, the only trimester with two vacancies is F17, so 308 and 332 must be taken in F17.

The remaining non-Sudoku vacancies are in S18, F18, S19, and W19–20. 289 has to be taken in a trimester immediately before and after Sudoku seminars. Since there are no Sudoku seminars in W18–19 or F19, 289 must be taken in S18. Furthermore, since 176 must be taken the semester immediately after 438, 176 must be taken in F18 and 438 in S18 (and 468 must be taken five semesters after 438 in W19–20). Since 234 must be taken before 180, they are taken in S19 and W19-20 respectively.

440 must be taken in Winter, and three Winter semesters are full, so 440 must be taken in W17–18. 475 must be taken in Spring; S18 is full, 475 conflicts with 234 in S19 and with 504 in S21, so it must be taken in S20.

474 is not offered in the Spring and conflicts with 332 in F17 and with 176 in F18, and so 474 must be taken in F20. 426 and 421 must be taken in the same academic year, so they must be taken in F18 and S19; since 426 conflicts with 397 in F18, it must be taken in S19 and 421 in F18. The only trimesters left for 402 and 428 are F17 and S21, and since 402 must be taken before 428, 402 and 428 must be taken in F17 and S21, respectively.

Acceptance Letter to MIT	Anger Management Book	Architect’s Compass	Bargaining Chips	Broken Twig	Burnt Sulfur Lugnut	Cardiac Devices	Denial of Service Attack Plan
Depression-Era Clothing	Domestic Avocado	Faded Sofa	Fancy Pocketwatch	Harlequin Doll	Iron Shovels	Leviticus Single	Lil’ String Bikini
Little Statue of Liberty	Lottery Numbers	Madman’s Jackal Mask	Mint-Flavored Salami	Mississippi Collectible	Nebular Gloves	Neural Blade	Officer’s Truncheons
Old Deuteronomy Sheet Music	Polyatomic Robot	Red Pinafore	Sega Genesis	Severe Beret	Shield of Judgment	Sienna Notebook	Soldierly Parasol
Sparkling Necklace	Super-Accurate Tri-Square	Tacky Jeweled Helm	Tamil Liqueur	Ultima III: Exodus	Ultrasonic Boots	Unsafe Mtorolite	Worn Loop of Gold
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