CLUE 8- SOLUTION

In typical Team Mystic Fish over-analysis, we noticed typos on the Coleridge quotation and tried to read meaning into them. For example, the word "subtlest" was missing the first "T" and "mathematical" was missing the "H." Hmmm.... could that be TH for "Treasure Hunt?" or TH as in the start of THC? (After all, this was the 420 game.) No, to paraphrase somebody-famous-or-other, "sometimes a typo is just a typo."

This first sheet shows F(n) = y, where y = the number of areas into which you divide a circle by connecting each of n points on its circumference with every other point.

The formula is:

F(n) = 1 + C(n,4) + C(n,2)

C(n,k) is also known as "n choose k" and equals the number of unordered combinations of n items taken k at a time. C(n,k) = n! / [k! * (n-k)!]

n! is also known as "n factorial" and equals n * (n-1) * (n-2) .... * 2 * 1

A discussion of this formula can be found at http://cut-the-knot.com/Generalization/cuttingcircle.html and also at http://forum.swarthmore.edu/dr.math/problems/shah5.19.98.html.

{click on the image to see it full-size - it's clearer when it's larger}

The second sheet is the cipher that has to be solved to reveal the next clue location. Because the first sample sheet only shows f(n) up to n = 6, but the cipher calls for us to know the values f(n) for n as large as 42, we needed to find the formula or someone who could give us the values. Fortunately Kiran Kedlaya, our mathematician teammate who couldn't play this time, was home and played phone-a-friend; he had the information at his fingertips, so he read us the values.

 n F(n) mod(F(n),26) n F(n) mod(F(n),26) n F(n) mod(F(n),26) 1 1 1 15 1471 15 29 24158 4 2 2 2 16 1941 17 30 27841 21 3 4 4 17 2517 21 31 31931 3 4 8 8 18 3214 16 32 36457 5 5 16 16 19 4048 18 33 41449 5 6 31 5 20 5036 18 34 46938 8 7 57 5 21 6196 8 35 52956 20 8 99 21 22 7547 7 36 59536 22 9 163 7 23 9109 9 37 66712 22 10 256 22 24 10903 9 38 74519 3 11 386 22 25 12951 3 39 82993 1 12 562 16 26 15276 14 40 92171 1 13 794 14 27 17902 14 41 102091 15 14 1093 1 28 20854 2 42 112792 4

After taking the values Kiran we gave us, we converted each number to mod(26). In other words, we kept subtracting 26 from it until we got a number between 1 and 26. Then we took the operations on the second sheet and applied them to those numbers. In other words, when the second slip said F(5) - F(31) we calculated mod(F(5),26) - mod (F(31),26). We could have just subtracted F(31) from F(5) but then we would have had to convert a negative number to a letter. Easier to do the mod(26) first. The final step to get the answer in plain text was to convert the resulting numbers to letters, where for example if the number result was 6, the corresponding letter was the sixth letter of the alphabet (F).

 Operation mod(F(n1),26) mod(F(n2),26) Result Letter F(28) + F(29) 2 4 6 F F(15) 15 15 O F(19) 18 18 R F(6) 5 5 E F(30) - F(2) 21 2 19 S F(35) 20 20 T F(41) 15 15 O F(9) - F(1) 7 1 6 F F(13) 14 14 N F(24) 9 9 I F(27) + F(33) 14 5 19 S F(7) 5 5 E F(27) 14 14 N F(42) + F(39) 4 1 5 E F(20) - F(33) 18 5 13 M F(40) 1 1 A F(19) 18 18 R F(26) - F(25) 14 3 11 K F(16) + F(28) 17 2 19 S F(21) + F(22) 8 7 15 O F(26) 14 14 N F(32) 5 5 E F(12) 16 16 P F(35) 20 20 T F(35) 20 20 T F(34) + F(41) 8 15 23 W F(15) 15 15 O F(5) - F(31) 16 3 13 M F(23) 9 9 I F(18) - F(3) 16 4 12 L F(31) + F(2) 3 2 5 E F(20) + F(1) 18 1 19 S F(5) 16 16 P F(39) 1 1 A F(15) + F(42) 15 4 19 S F(36) - F(2) 22 2 20 T F(7) 5 5 E F(26) 14 14 N F(18) + F(3) 16 4 20 T F(20) 18 18 R F(34) - F(22) 8 7 1 A F(26) 14 14 N F(38) 3 3 C F(33) 5 5 E F(37) - F(35) 22 20 2 B F(11) - F(22) 22 7 15 O F(41) 15 15 O F(17) - F(14) 21 1 20 T F(4) 8 8 H F(15) 15 15 O F(10) 22 22 V F(8) - F(18) 21 16 5 E F(35) - F(28) 20 2 18 R F(20) + F(14) 18 1 19 S F(35) 20 20 T F(7) 5 5 E F(21) - F(38) 8 3 5 E F(3) + F(4) 4 8 12 L F(9) - F(7) 7 5 2 B F(20) 18 18 R F(24) 9 9 I F(3) 4 4 D F(22) 7 7 G F(33) 5 5 E

FOREST OF NISENE MARKS
ONE PT TWO MILES PAST ENTRANCE
BOOTH OVER STEEL BRIDGE

OK
At this point things didn't go quite as planned, so I have to give you some background information here.

After we entered the Forest of Nisene Marks, we were supposed to go over the steel bridge mentioned above, which we did. There was a phone booth by that bridge. Tracking us with our GPS transmitters, GC would know exactly when we reached the bridge and were going to call us on that phone. In the dead of night, traveling very slowly on an extremely bumpy dirt road, we were bound to hear the phone ring and pick it up.

At that point, they were going to tell us that the Women in Red were enemy agents from the Matrix and that we should go to the Santa Cruz Lighthouse to disable their vehicle (but first, we should pick up our next clue and a bag of food - bread, salami, cheese, etc, which we really appreciated!).

Unfortunately this very cool clue didn't work out as planned because the phone at the phone booth had stopped working before we got there. So GC called us on our cell phone instead and told us about the Women in Red.

Coincidentally, our team had just been speculating about the Women in Red team. First, GC had been telling us every time we called in that the Women in Red team were in the lead. And they had been leaving behind 3x5 cards with lipstick kisses on them (teams do that to taunt the teams behind them - they leave behind customized team tokens). We were suspicious because they had written the best java game agent, they had led the game for 20 hours, yet they were a rookie team??? So when GC told us that they were "Matrix agents" we weren't surprised.

Clue 9