At the end of the trip you will have six numbers which will enable you to find the location of the cache. The numbers can be collected in any order. Please be careful as you go, whether walking or in a vehicle, as all are adjacent to roads, with the main road and the road to the garden centre being particularly busy in the morning and evening ‘rush’ hours.
The final location is at N50o 13.ABC W005o 05.DEF
Quadratic Equations
ax2 + bx + c = 0
Location 1 (N50 13.345 W005 05.117) - To find ‘a’ you need the second number embossed on the back of the green ‘Public Footpath only’ sign starting ‘CL-a--’.
Location 2 (N50 13.531 W005 05.319) - There is a fire hydrant sign attached to the street name . ‘b’ = 10 – (Top number/Bottom number).
Location 3 (N50 13.284 W005 05.348) - On the post box below the slot is a ‘Last Collection Time’ notice. ‘c’ = the third number in the time for the Saturday collection.
Insert the numbers into the quadratic equation above and solve for x. ‘A’ = x + 3.
Divide and substitution
Location 4 (N50 13.498 W005 05.133) - On the corner of the road between two green boxes is a fire hydrant sign, you need the numbers on the sign. To find ‘B’ you will need to find ‘E’ so it can be substituted into the following equation.
‘B’ = (Top number / Bottom number) – ‘E’
Area of a Triangle
Location 5 (N50 13.390 W005 05.243) - Each post box has a Postbox No. To work out the Area of the triangle you will need two numbers from this No.
Base length ‘b’ = first Postbox No. number and the Height ‘h’ = fourth Postbox No. number. Area = ‘C’
Straight Lines
Location 6 (N50 13.341 W005 05.477) - Every straight line can be represented by the following equation y=m x + b, where ‘m’ is the gradient and ‘b’ is where the line intersects the ‘y’ axis. Now, if ‘m’ = number of red arrows on the path side of the footpath post and ‘b’ = the number of red arrows on the road side of the footpath post solve for ‘y’ when ‘x’ = 2. y = ‘D’.
Just a number
Location 7 (N50 13.308 W005 04.893) - On the post box what is the third number of the Postbox No. = ‘E’. This number is also the ‘substitution’ required to work out ‘B’.
Right Angled Triangles
Location 8 (N50 13.296 W005 05.582) - There are two hydrant signs at this location. When looking directly towards the street name plate, the vertical length of a right angled triangle is the bottom number on the LEFT hydrant sign and horizontal length of the triangle is the bottom number on the RIGHT. Using these two numbers work out the hypotenuse (sloping side) length AB = ‘F’.