Pathfinder 1997
Route Card Solutions

Section 1
A fairly obvious clue was in the title. Go OUT of km squares using WHITE roads. The numbers referred to the grid line that you crossed on the white road. The PCs were located at each of the clues except for the 26, 12 crossings. If you got one wrong here it was probably the 14 crossing - you should have used the A road layby rather than the longer white to the North.

Section 2
Fuse (Electricity) Boxes (km squares). The numbers were the number of times that you crossed an ETL in km squares. The eight PCs were located at 42(1422), 37(1725), 51(1427), 3rd ETL Crossing(1429), 150 289.5 (the tricky one, which quite a few missed) , ETL on White(1528), Telephone (1726), 25(1824).

Section 3
It shouldn't have taken too much effort to work out that the colour sequence of the roads to visit was:

W, R, W, Y, W, R, W, Y, W, R, W, Y, W, R, W, Y, W, R, W, Y, W, R, W, Y, W, R

The trickier bit was than finding the shortest route using this information. This was pretty difficult to mark. To make things easier there were 12 PCs after all each worth 50secs. These were located at the entrance and departure to each yellow road visited as follows:

WSW210.5 242NNE, SSW210.75 242.75ESE, N217.75 237.25E, S221.75 240.5W, SSE231 249ENE, WSW231.5 249.5SSE, S238.25 246.25W, SE237.75 246.5WSW, E228.5 260.5S, N228 258E, WSW225.5 259.75NNW, SSE225.25 260WSW. The white at 224.5 239.5 doesn't go.

Section 4
Number the through-roads that leave a km square starting in the top left hand corner and going clockwise. The clues then referred to the numbered exit from consecutive km squares. PCs @ S215 277.5E, WSW211.5 294.5NE, S237 279.75SE, W254 278N, NNW260.5 290.5E, N281 281.5E.

Section 5
German bits from the map legend were the theme here. H = Hauptstrasse (Red), N = Nebenstrasse (Orange), S = Strasse (Yellow), SS = Sonstige Strasse (White). Having got through the translation, it was then a matter of correctly identifying which bits were S or SS. For example the sequence NSSSN. Was this Orange, Yellow, White, Orange or Orange, White, Yellow, Orange? The former because it was shorter. The PCs were usually at the entrance to each white road visited. If you got a few penalties it was probably because you missed PC3 in the A road lay-by. The PCs were at:

E266.5 250N, W265.5 249.5S, WNW259.5 247.25SSE, NE262.5 222.5SW, E241.5 222.5S, N224.75 197.25NNE, W245 185S, SW279.5 180SE, WSW294.25 197.5ENE, SE291.5 216.5NNE

Section 6
A bit of obvious guess work and process of elimination would have given you the results of the matches, where the scores were equal to spot heights on the map. Most of you got this one. You should have ended up with following sequence of spot heights (each a PC) to define the route:

48, 55, 7, 6 (two possibilities about the same distance), 26, 39, 6, 8, 6, 22, 18, 16, 27, 8, 19, 28, 6, 6, 28, 23, 77, 69, 67, 22

Section 7
A code, where the number of letters in each phrase gave you the digits of the via map references (each a PC). For example, The (3) Large (5) Map (3), Go (2) To (2) Braintree (9). The colours translated to numbers to give you fractions, where Yellow=1, Green=2, Red=3, Blue=4. Easy for most of you.

Section 8
(Secondaryroad)(peaks) = (B)(ridges). In other words, crossing bridges on coloured roads where capitals referred to (Over) and lowercase (Under). Some missed the the loop over the yellow bridges in 4419 and 4418. The PCs were at the following underlined/italicised crossings

W W Y Y Y W R r R y Y W Y O O y W O Y y Y Y Y r r r R

Section 9
Crossing Odd and Even grid lines. The correct sequence was:

47, 46, PC, 16, 16, 16, 45, 16, 44, PC, 16, 44, 44, PC, 43, 43, 16, 43, PC, 43, 15, 14, 44, PC, 44, 43, 13, PC, 13, 42, 41, PC, 41, 13, 42, 12, 43, PC, 43, 11, 42, 10, 42, 43, 09, PC, 09, 44, 10, 11, 12, PC, 12, 12/45, 13

Section 10
A herringbone where only the no-through-roads were shown. PCs were placed at:

464 149.25, 466 146.5, 469.25 150, 471.5 145.5, 490.25 120.25, N477.5 108.5SSE, 475.75 096, 470.75 096

Section 11
The numbers were the trigonometric values of sines, for example sine(36) = 0.5877852522925 (approximately!), so far so good. Then the 36 referred to product of the digits of a spot height to be visited, i.e. 9 x 4 = 36, which caused the problem. There was a PC at each spot height. The correct sequence was:

94, 154, 138, 118, 112, 163, 127, 178, 93, 136, 143, 107, 128, 99, 101

Section 12
From the bottom left corner you had to traverse the board moving like a Knight chess piece, visiting each square once only. Warndorff's rule states that "at each stage of the knights tour, one must choose the square with the fewest remaining exits". For the nerds, this can be found in The Journal of Recreational Mathematics, 1:225-233, 1968 or at http://homepages.enterprise.net/stevegray/tour.html on the Internet, although many specialist chess books also have the solution to this problem.

If you number the y-axis from 1 to 8, and letter the x-axis from A to H, the correct tour was

A1, B3, C1, A2, B4, A6, B8, D7, F8, H7, G5, H3, G1, E2, G3, H1, F2, D1, B2, A4, B6, A8, C7, E8, G7, H5, F6, G8, H6, G4, H2, F1, D2, B1, C3, E4, C5, E6, D8, B7, A5, C6, A7, C8, E7, D5, F4, D3, E1, G2, H4, F3, D4, F5, E3, C2, A3, B5, D6, C4, E5, F7, H8, G6.

Making this into a string of numbers yielded spot heights to visit on route thus:
109, 86, 49, 49, 43, 63, 87, 73, 54, 32, 55, 35, 31, 77, 65, 52, 55, 39, 89, 53, 84, 116, 69, 41, 86, 66, 85, 131, 98, 223.

There was a PC at each spot height. The PC at the second 49 spot height was scrubbed because it was outside of the designated plotting area (sorry!)

Section 13
Again, there was a clue in the title. The numbers were coded with different numeric bases starting from binary (2) up to hexadecimal (16) and back down to binary (2). The resultant decimal numbers were grid lines to cross thus:

37, PC, 36, 10, 35, 35, 11, PC, 35, 34, 11, 33, 32(PC), PC, 31, 31, 10, 31, PC, 09, 31, 09, PC, 32, 10, 33(PC), 10, 10, 34, 10, PC, 9, 35, 35, 9

Section 14
More spot heights, this time by showing the relationship between the senior digits and the junior digit as follows:

147 (14+7=21), 205 (20/5=4), 231 (23-1=22), 195 (19*5=95), 72 (7-2=5), 101 (10+1=11), 69 (6*9=54), 116 (11+6=17), 132 (13-2=11), 91 (9/1=9), 149 (14+9=23), 119 (11-9=2), 188 (18-8=2), 156 (15*6=90), 124 (12/4=3)

There was a PC at each spot height. This was just a variant on "digit themes" often used with spot heights, but was only cleaned by 4 entrants! If you got one PC wrong it was probably sh188 - you have to come via 3007 to correctly visit it.

Section 15
Sorry, this was nothing to do with directions, although it was obviously disguised to be. Study the kilometre squares in the area and highlight the ones containing the capital letters NEWS. For example, 3101 has M(S) and (W)aggs Plot, so the square is described as SW.; 3499 has (E) (S)ub and (S)couse. The squares to visit were:

3101, 3201, 3301, 3201(PC), 3200, 3300, 3399(PC), 3499, 3498(PC), 3398, 3397, 3497, 3498, 3497(PC), 3498, 3598, 3498, 3499(PC), 3400, 3500, 3600, 3700, 3701(PC), 3702, 3802, 3902, 3901, 3900, 3800, 3899, 3799(PC), 3700, 3600, 3699, 3599, 3598(PC), 3597, 3596, 3595

Section 16
A tour of gradient arrows. The compass points referred to the direction in which the gradient was pointing. PCs were at the following underlined gradients

SSE, SSW, N, E, NE, WNW, ESE, E, NW, NNW, W, SE, SE, S, S, S, S, NNE, N, SSW, WSW, NNW, ENE, W, SE, ESE, N, NNE

The most common mistake was not taking a shortest route via NE335.75 918.5NNE.

Section 17
Do the first doughnut then the second. Each segment was colour coded according to the sections of coloured road that had to be used. The first started at the bottom left with the sequence Red, Red, Red and went clockwise. The second started at the bottom with Yellow, Yellow, White, Orange and went clockwise. Actually the plot went out of the designated plotting area along the Seaton sea-front, otherwise it wouldn't work, but quite rightly you chose to ignore that. The PCs were at:

SE292 913.5E, 299 922.75, NW285.25 917.75WSW, NNW132WSW, S267.5 980E, E270.25 911.5NE, WNW259 911.5S, E247.5 898.75N, 232 900, SW238.75 903NNW, 235 915.5, 233 913.25

Section 18
Working through the grid from left to right the colours referred to features crossed en route. Doesn't need much more explanation - the most successfully completed route card.

Section 19
More coding of colours to numbers giving spot heights. 0 (black), 1 (red), 2 (yellow), 3 (green), 4 (cyan), 5 (blue), 6 (magenta), 7 (white), 8 (light grey), 9 (dark grey) yielding the following sequence (underlined = PC):

48, 22, 71, 13, 4, 4, 7, 9, 8, 72, 14, 55, 48, 107, 116, 82, 58, 115

Some tried to visit sh111 rather than 116, but if look very closely, you'll see that the "6" colour is different. To visit 115 correctly you had to approach via GS 2399.

Section 20
G = Gridline, Gradient or Graticule, T = Telephone, S = Spot Height, B = Bridge. You probably got that bit OK, then the next problem was sorting out the gridlines from the gradients for the shortest route. This was hindered a bit by the sh 105 in 2704 being missing from the sequence, but you sussed that to make it work. A few lost their way near the end by choosing a longer route than was necessary. The route was:

G, 23, T, G, PC, G, G, PC, 24, G, PC, 04, 25, 04, B, 04, 26, PC, 04, G, G, 27, G, PC, 04, G, 105?, G, T, G, 27, 05, 27, 27, 196, 06, PC, 06, 26, G, B, 71, 25, 05, 87, T, 24, Graticule, G, B, 23, PC, 23, 05, G, G, 24, PC, 06, 105, 07, 114, 07, 07, 24, 07, 171, 23, G, 06, PC, 06, 22, 257, 06, 05, G, 21, G, 05, 06, G, 06, PC, 06, G, G, PC, 07, T, 08, 09

Section 21
My personal favourite, but the most hated route card. Most definitely the one which decided many of the top places and correctly solved by only 4. You had to treat this just like a series of crossword clues (as usual with crosswords, single squares do not count) to discover a series of grid line "Crossings". Moving left to right you have the following clues:

1 across (right), 1 down, 1 left, 1 right, 1 left, 1 down, 3 across, 2 up, 1 right, 1 left, 1 up, 1 left, 1 down, 1 left, 1 left and up (i.e. a grid line intersection), 1 right, 1 left, 1 right, 1 left, 4 up, 2 right, 2 up. These movements refer to how you exit consecutive grid squares. Converting them to the more normal direction convention you go:

PC, E, S, W, PC, E, W, S, PC, E, E, E, N, PC, N, E, W, N, W, S, PC, W, N/W, E, W, W, PC, N, N, N, N, E, PC, E, N, PC, N

Section 22
The letters represent the colours of the roads you are to use, except that the letters of the words move one to the right with each usage. So your correct sequence was:

(Y)ellow, (O)range, PC, (W)hite, Y(e)llow, O(r)ange, Ye(l)low, PC, W(h)ite, Yel(l)ow, (R)ed, Yell(o)w, PC, Wh(i)te, R(e)d, PC, Whi(t)e, Re(d), Yello(w), Whit(e), (Y)ellow, PC, (W)hite, Y(e)llow, PC, W(h)ite, Ye(l)low, PC, Wh(i)te, Yel(l)ow, (R)ed, Yell(o)w, PC, Whi(t)e, R(e)d.