# Endgame Logic Puzzle – Who Had Means?

## by Dave Shukan (with Round One puzzles by Kevin Wald)

Teams need to determine which three suspects out of:

John Alafontaine
Alan Caster
Elihu Leather
Samantha Oriflamme
Jan Plumb
Marcia Taylor
Betty Wexter

wrote which of the three puzzles (A-C) accompanying Dr. Awkward's cover letter during which months of 2007. Only those suspects had the means to kill Dr. Awkward (the knife used in Round One of the ostensible Hunt), and matching the suspects to their specific puzzles and months will cause the witnesses to admit your conclusions are correct.

### FACTS FROM JANUARY 4, 2008 COVER LETTER FROM DR. AWKWARD:

C1 – One week after the end of the 2007 Hunt, all 7 people and Dr. A had a dinner at which they discussed the planning of the 2008 Hunt. Thereafter, each of the three puzzles was written by exactly one writer from among the listed seven, all of whom were different. Dr. A handed each writer an assignment at noon in his office on the MIT campus on the first day of a month (a different month for each writer), and each writer handed him a finished puzzle in person at noon in his office on MIT campus on the last day of the same month the writer received the assignment. No changes were made to the puzzles after they were submitted.

C2 – No writer was born within the same calendar year, and the writers were not all the same gender. No one wrote a puzzle during the month of their birthday.

C3 – One of the writers started working on her puzzle on Friday the 13th after being inspired by the day to include a reference to bad luck in the puzzle, and stopped by Dr. A's office that afternoon.

C4 – Every weekend of 2007 Dr. A took at least one day (Sat, Sun, or both) completely off and away from campus.

C5 – The author of Puzzle A worked on it a little each day for more than four weeks.

C6 – At least one puzzle was worked on, in whole or in part, during winter.

C7 – All suspects had become enemies by the time of the cover letter.

C8 – No suspect turned in a puzzle after becoming an enemy.

### THE THREE PUZZLES ACCOMPANYING THE COVER LETTER:

Puzzle A ("Just Fueling Around") – contains a reference to bad luck.

Puzzle B ("Fortune") – contains a reference to bad luck and refers to facts from March 2007 (DeGeneres nominations, Jeni passing) such that it could not have been written in February.

Puzzle C ("Some Scrambled Word Game") – refers to a fact from April 2007 (Imus cancellation) such that it could not have been written in March.

### FACTS FROM DOSSIERS:

D1 – The birthdates of the suspects are as follows:

Jan – January 22, 1980
Betty – January 8, 1972
John – August 19, 1972
Alan – March 3, 1984
Marcia – December 12, 1980
Elihu – February 15, 1972
Samantha – November 28, 1951

D2 – Throughout 2007, Samantha was bicoastal, always spending alternate entire weeks on the east and west coasts of the United States, and always taking an overnight flight to travel between, leaving Saturday night after dinner and arriving Sunday morning before breakfast.

D3 – John became an enemy before Alan did.

D4 – Dr. A and Alan were away from the MIT campus at noon on May 31. Sometime during the summer of 2007, Alan became an enemy of Dr. A.

D5 – During MIT IAP 2008, at some point before the start of the 2008 Mystery Hunt, Samantha hosted a party at her apartment, and Jan, Marcia, and Elihu (but not Betty, John, or Alan) attended. The three puzzle writers were not all together at the event.

D6 – Elihu became an enemy during Thanksgiving 2007.

D7 – The fourth occasion on which Jan saw Dr. A during 2007 was the morning on which Jan became an enemy.

D8 – Alan was not in Boston at noon on August 31, 2007 (he was in San Diego shortly before the start of San Diego's 6 to 4 win over the Dodgers).

D9 – Samantha did not write the August puzzle.

### SOLUTION:

(1) First, solve for months of puzzles –

M1 – By C1, there is no puzzle in January. Everyone is known to have become an enemy before noon on December 31 except Marcia and Samantha (Betty was on some Saturday before January 4, 2008), but Samantha is bicoastal and thus could not do December (1 and 31 on different coasts) and Marcia was born in December so could not do December, thus December was not a puzzle month.

M2 – By C5, Puzzle A was not written in February, and since Puzzles B and C reference events occurring after February 2007, they were not written in February, so February was not a puzzle month.

M3 – By C3, at least one of April and July was a puzzle month (only those 2 had a Friday the 13th).

M4 – By C6, since there was no puzzle in JAN, FEB, or DEC, March was a puzzle month, so by C4 April cannot be one (March 31-April 1 = Sat Sun), so by M3 July was a puzzle month. By C4, since July was a puzzle month, June cannot be one (June 30-July 1 = Sat Sun).

M5 – Combined with yes MAR and JUL, and no JAN, FEB, APR, MAY (by D4, Dr. A was not at MIT on May 31), JUN, or DEC, the remaining puzzle had to have been written in AUG, SEP, OCT, or NOV.

Thus, the puzzles were written in MAR, JUL, and AUG/SEP/OCT/NOV.

* * *

(2) Assign puzzles to months –

JULY – C does not have a bad-luck symbol, so cannot be July. A was worked on for at least 4 weeks, but the July puzzle was started on July 13. Thus, B = July.
MARCH – C refers to an event after March, so cannot be March, so March must be A.
AUG/SEP/OCT/NOV – must therefore be C.

* * *

(3) Then solve for writers –

X1 = By D4, the only puzzles that Alan could have written are before September, which is only MAR or JUL or AUG. But it cannot be MAR (Alan was born in MAR), and JULY was written by a female (reference to "her" in C3), and cannot be AUG (by D8), so Alan is not a writer.

X2 = By D5, there were not three writers among Jan, Marcia, Elihu, Samantha. If Elihu is a writer, then Betty and John (both born same year as Elihu) could not be, and we know that Alan is not (from X1). Thus, if Elihu is a writer, Jan, Marcia, Elihu, Samantha would contain 3 writers, which is inconsistent with D5. So Elihu is not a writer.

X3 = With Alan and Elihu gone, John must be a writer (since at least one writer was male), and thus Betty, who was born in the same year, is not. Thus, writers are John, Jan/Marcia (born in same year), and the one remaining slot must be Samantha.

X4 = John became enemy in September at the latest (D3) and was born in AUG, thus cannot have written the final puzzle, and a female wrote JUL, so John wrote MAR.

X5 = By D2, Samantha's month cannot be SEPT (1st and 30th would be on different coasts), and by D2+C3, the writer being on campus on Friday the 13th means Samantha cannot be JUL (since she would have been on the west coast on the 1st), and Samantha's month cannot be NOV (her birth month), and MAR is taken by John, and by D9 she is not AUG, so Samantha is OCT.

X6 = The writer of JUL (only Jan and Marcia remain) had to see Dr. Awkward on at least 4 occasions during 2007 before the writer became an enemy – the kickoff dinner (C1) and 3 times in JUL (1st, 13th, 31st). Thus, Jan cannot have written JUL, since she only saw Dr. Awkward on only 3 occasions during the year before becoming an enemy before noon on the fourth occasion (D7). Thus, Marcia wrote JUL.

Thus, writers are: MAR = John, JUL = Marcia, OCT = Samantha.

* * *

(4) And, matching up puzzles and writers according to month:
"Just Fueling Around" was written by JOHN ALAFONTAINE in MARCH.
"Fortune" was written by MARCIA TAYLOR in JULY.
"Some Scrambled Word Game" was written by SAMANTHA ORIFLAMME in OCTOBER.

"Just Fueling Around" was written by JOHN ALAFONTAINE in MARCH.
"Fortune" was written by MARCIA TAYLOR in JULY.
"Some Scrambled Word Game" was written by SAMANTHA ORIFLAMME in OCTOBER.