Partial solutions to the Star Caches. Star Traversal (GC41A1F) permutation 0123456789 inverse 0123456789 0891273564 0346978512 Looking at the original permutation we can grt the inverse: 0->,1->3, etc. Then apply that to the given coordinates. given N 44° 95.213 W 093° 87.064 final N 44° 27.436 W 093° --.--- Fallen Star (GC41HPV) This might be the easiest puzzle, but it has the most interesting hide. One common wat to draw a five pointed star is to start at the point at the top and then draw a line to the point toward the southwest, and hence to the only poine accessible from there, and so on. In so doing pick up the numbers along the way the first time they're encountered, viz. 2-7-4-3-6-... . Half Solution = N 44° 27.436 Team of 10 (GC41HQ5) Folks seem to have an easy time with this one too. Four of the assignments were given in the description. In the chart, it appears that C should be probably be assigned to Cache#0. Eliminate the C row and #0 column. In the remaining table it appears that I = #3 might work. Continue in this fashion. If an ambiguity develops you might need to try more than one assignment to get it to work. Half Solution = N 44° 26.078 Haiku (GC41HQ3) This uses a 5-choose-2 code. Say there are five vowels AEIOU. These can be taken two at a time in ten ways: {A,E},{E,I},{A,O},{A,U},{E,I},{E,O},{E,U}, {I,O}, {I,U}, and {O,U}. Let these be encoded by 0,1,...,9 resp. Each of the ten words in the poem contains two vowels. Consider the first word, ROADS, which contains {A,O} and so get assigned a '1'; HUNDRETH -> {E,U} -> '6', etc. Half Solution = N 44° 26.450 Oops (GC41HQ6) This cache is based on the bar code for U S postal zip codes and their check digits. So if you google such things as "zip codes", "postal codes", "postal codes", you come up with appropriate web sites. But the explanation below might be sufficient. The bar code for zip codes is a 5-choose-2 code, so called because in each group there are five bars of which two are long bars. Let's user a 1 for a long bar and a 0 for a short bar. Then the 10 patterns possible are: 00011,00101,01001,10001,00110,01010, 10010,01100,10100 and 11000. To get these to correspond to the 10 digits 0 to 9, 7-4-2-1-0 base is used. For example, for 00011 the consecutive bit are multiplied by 7,4,2,1,0 giving 0x7+0x4+0x2+1x1+1x0 = 1, so 00011=1. Then 00101=2+0=2, etc. And finally for 11000 we get 7+4 which will be taken to be 0. Let's consider the North code: 10010101100011101001000101100011 which we'll rewrite first line as the first line below in which parentheses are used for separation. The 1's at the ends are "guard bits". In between there are six groups of five bits each. The first five are for the zip code; the sixth (10001) is the check digit. Note that the third group (01110) is not valid because it contains three rather than two 1's. For the five valid groups I've written the basis 74210 string just below each group and the corresponding decoding below that. (1)(00101)(01100)(01110)(10010)(00101)(10001)(1) (74210)(74210) x (74210)(74210)(74210) 2+0 4+2=6 x 7+1=8 2+0=2 7+0=7 So far we have 26.x82. But it remains to determine x. This it where the check digit comes in to play. The sum of all the digits, including the check digit, must always add to a multiple of 10. Thus 2+6+x+8+2+7=25+x=30 only if x=5. So the third group (01110) should have been corrected to be (01010).Thus we see that Half Answer = N 44° 26.582. West can be determined similarly, except that there's a 0 where there should have been a 1. 10 City tour (GC41HQ9) It's best to have solved Oops first. The 10 City Tour solution requires several steps. First arrange the 10 cities in a big circle and the most efficient circuit should become obvious. (The "Traveling Salesman Problem" in general can be very difficult but for this instance is quite easy.). Next we need to assign digits to the cities. This can be done using the check digits for their zip codes. (See Oops above). Finally you need to determine where to start the tour and whether to go clockwise or anti-clockwise. Half Solution: N 44° 27.435 RECENT RATS (GC3ZHMY) In some ways this is the easiest of the whole bunch. "RECENT RATS" is an anagram of "STAR CENTER". The permutation in the hint is simply the one which will transform "RECENT RATS" into "STAR CENTER" and no other use for the problem. If that's all you were missing go solve the problem. Otherwise, the star center being referred to is the center of the 5-pointed star comprised of the 10 given coordinates for these 10 puzzles and listed as additional waypoints. As the star is symmetrical about a vertical line running through Star Traversal and RECENT RATS itself, the West coordinate is simply that of those two, i.e. Half solution: W 093° 15.092 To get the North component you'll need to average the latitudes of all ten points, or of just the five out-points, or of just the five in-points. Star Traversal (GC41A1F) The relevant permutation written in the two line form is 0123456789 inverse is 0123456789 0891273564 03469----- Given: N 44° 95.213 W 093° 87.064 Half Solution: N 44° 27.436 W 093° --.--- Perfect Shuffle (GC41HPY) Half Solution: (N 44°) 26.564 Given: (N 44°) 28.640 where successive digits were encoded using the successive colmuns. The 0th column makes no changes so 2->2. The 1st column takes 6->8. The 2nd column takes 5->6; the 3rd 6->4, and so on. Bowling Pins (GC41D84) this turns out to be the most difficult one. The relevant permutation and its inverse are 0123456789 inverse 0123456789 7890631245 3675894012 What was in position 0 (the 0) goes to position 7. What was in position 1 (the 9) goes to position 8. What was in position 2 (the 8) goes to position 9. What was in position 3 (the 2) goes to position 0. What was in position 4 (the 5) goes to position 6. And so on. position: 01 234 56 789 Given: N 44° 09.825 W 093° 47.361 Half Solution: N 44° 2-.--- W 093° -5.098 Starfish (GC41HQ0) As this involves both substitution and transposition, one might think it would be the most difficult. However, as in the example the relevant permutation is its own inverse and decomposes into simple cycles. In two-line form the permutation (and its inverse) is 0123456789 8765432109 In cycle form it is (0 8)(1 7)(2 6)(3 5)(4)(9) Consider the 1 in position 0; it becomes a 7 and moves to position 8. Consider the 2 in position 1; it becomes a 6 and moves to position 7. Consider the 6 in position 2; it becomes a 2 and moves to position 6. And so on. position: 01 234 56 789 Given: N 44° 12.673 W 093° 74.168 Half Solution: N 44° --.--- W 093° -2.67-