Games Mag Oct Contest Error (***SPOILER***)

Games Magazine's October issue is running a contest called 'Common Factors', a devilish multi-layer puzzle involving presidential trivia, ZIP code numerology and US county seats.

I've been about 3/4 obsessed with solving it for months, but I'm stuck on what I think is an error of the puzzle maker's.

I'm posting here because while Games is still published, a) they list no email address or website, (probably to avoid cranky mail like this); b) even if I did go to the extraordinary effort of writing this on paper, putting it in an envelope with a Bennington stamp and mailing it, the editors would just ignore me; c) readers of rec.puzzles are the only people in the world who would possibly care. {The best way to get Games is to subscribe: Games Mag, PO Box 144, Ft. Washington, PA 19034}

If the complicated formula is solved with the values I've found, it does not divide evenly, but there is an incorrect solution nearby that I think they used, since it points to a city with 'Sioux' in its name.

First the problem, then my reasoning and the details.

Problem 16: Town whose ZIP code is (Y^2/2T^2) x (3T+2) - (PxL), where, on a United States stamp on which is printed the name of one of the 25 towns in this puzzle, issued the day before the (L^2 x (L+1) + 1)st anniversary of the death of the successor to the president used to determine L in this clue, Y is the year printed on the stamp that dates the depicted object T is the number of items on that object whose anagram is TRAIN STOPS.

L is the same as in clue 7, except using the last name only, and P is the largest prime factor that is smaller than the largest prime factor of the ZIP code of the answer to clue 21. ****SPOILER ALERT**** There was a stamp series issued on a date satisfying the problem for another president with a picture of the White House, but no date on stamp or anagram solution. Then I found the Bennington Flag, a US flag with an arch of thirteen seven-pointed white stars in the blue field.

Town whose ZIP code is (Y^2/2T^2) x (3T+2) - (PxL), where, on a United States stamp on US Flags Series: The Bennington Flag which is printed the name of one Bennington, Indiana of the 25 towns in this puzzle, issued the day before the 6/14/2000 (L^2 x (L+1) + 1)st 151st - L must be 4 or 5, since keyed to length anniversary of the of Pres names: 4=ford,bush,polk,taft -> 81st 5 5=tyler,adams,grant -> 151st if L=6 -> 253rd, too large death of the successor to successor(Tyler)=Polk, died 6/15/1849, 151 yrs the president used to determine L in this clue, Y is the year printed on the stamp !*!*!*! 1826 !*!*!*!

that dates the depicted object but 1820 fits the puzzle better. T is the number of items on that object whose anagram is TRAIN STOPS. STAR POINTS [this took an embarrassingly long time to solve]

L is the same as in clue 7, [president whose daughter was still alive on his 155th bithday] except using the last name only, [John Tyler, also president with most children 17, in clue 21] and P is the largest prime factor 883 that is smaller than the largest prime factor of 887 { this number runs throughout the puzzle} the ZIP code of the answer to clue 21. [answer supplied on request]

NOW THE MATH: (Y^2/2T^2) x (3T+2) - (PxL) Y=1826, but 1820 divides evenly. T=91 -> thirteen times seven STAR POINTS P=883 -> prime factor before 887, the common factor to class M L=5 -> tyler 1820^2 / 2*91^2 x (3*91 + 2) - 883*5 20^2 / 2 x (273 + 2) - 4415 , cancelling out the 91 200 * 275 - 4415 = 50585, which is the ZIP code for Sioux Rapids, IA.

The solutions of the 25 problems fall into 5 subsets of 5 related solutions: common factor of 887, 'Soiux' or 'Fort' in the name, last four ZIP digits the same. [I haven't figured out the fifth relation.] Using 1826, the date on the stamp, in the quotient leaves a remainder, a definite no-no in this type of puzzle. Substituting 1820 provides a cozy answer that fits the structure of the puzzle.

Tim Szeliga

40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

I haven't seen the actual stamp or a clear reproduction of it, but the USPS press release describing it says:

Bennington Flag c.1820 Long believed to date from the Revolution, the Bennington Flag was possibly made between 1810 and 1830. It could have been created during the War of 1812, or in 1826 to celebrate the 50th anniversary of the Declaration of Independence.

Perhaps the problem-setter read this and assumed that the date on the stamp must be 'c.1820', without actually seeing it. Alternatively, perhaps Tim knew of the date 1826 from an external source, and assumed that this must be the date on the stamp, without actually seeing it, when it's actually 'c.1820'. (Although Tim's reference to using the stamp suggests that the first case applies.)

I've finished the 23 ZIPcode puzzles and three of the replacements. Now I have to fit the answers into the contest diagram, grouping the nodes into five classes of five ZIPS, based on the path traced along the bridges linking the nodes. To find this Eulerian path, there must be exactly zero or two nodes of odd degree (# of bridges). In this puzzle, there are six, but we are required to remove one bridge and place it elsewhere. So, if we remove a bridge linking two odd nodes, like 15 & 21, and join up two other odd nodes, like 16 and 19, only the first odd node (Ft Leonard Wood, MO) and #4 remain. The rules state the starting point, so 4 is the ending.

We are to count along the path, assigning letters G-A-M-E-S as we go, so the first twelve and the last five are pretty much pre-determined. When we get to 19,

things get odd. I've got a good grouping, but only if I link 20 and 12, which requires severe stretching of the rules (and misses the 19-20 link).

There are some answers that could fit into multiple classes or have alternate, arguable solutions, but not so many that I can traverse the graph backwards and still expect them to fit. I guess some of my assumptions about Class Assignment Rules are wrong, which just adds to the richness of the puzzle, but I already caught one mistake, the Bennington Flag stamp. I have a GIF of the stamp that clearly says '1826', not 'c. 1820'.

Anyone wishing to discuss this puzzle offline are encouraged to write:

Tim Szeliga

{The best way to get Games is to subscribe: Games Mag, PO Box 144, Ft.Washington, PA 19034}