Have you ever seen a puzzle cache with a string of 0s and 1s and ignored it? We really want people to find our caches so we’ve decided to make this an easy to understand binary puzzle.
Basic binary is actually not that difficult. (Thanks are due to Zach Bacon for his excellent tutorial). It must be reasonably simple as we can now work out the basics! That said, we're a long way from becoming computer programmers so have no fear, this puzzle is very straightforward. You will soon be able to work out the clues, and who knows? It may be a first step to solving some of the fiendish binary puzzle caches out there.
Here goes……We are not mathematicians so please forgive the basic language used. But do read this as although it might seem basic, it helps to understand how decimal counting works first. In Decimal (Base 10), we use the single digit numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
We start at zero and increase each number by adding 1 to it until we get to 9 plus 1. We then have to create a new 2 digit number to express this as10 (or 1 set of 10 digits). As the decimal numbers get bigger we group them in other sets of 10, like 20 (2 sets of 10), or 70 ( 7 sets of 10). When we reach 10 sets of 10, we create a 3 digit number to write this as 100 (10 sets of 10),
It’s quite easy to see how this works on a car’s mileage clock
| Decimal |
100 000s |
10 000s |
1000s |
100s |
10s |
1s |
| 0 |
0 |
0 |
0 |
3 |
5 |
2 |
What are we actually reading when we see 000352 miles?
If you imagine the odometer on a new car reading 000008, when we drive another mile, the last column on the clock increases by 1 so we get 000009. The digit “9” means "one more than 8".
But when we drive another mile we've used up all the available digits in the Base 10 system - we have to start a new column. The odometer now reads 000010. This tells us that "you've driven ONE set of TEN miles". The second column is now called the "10's" column.
If we drive a bit further, and the odometer reads 000037, it is telling us "you've driven THREE set of TEN miles, plus 7 additional miles", for a total of 37 miles
Finally, when the odometer reads 000099, we've run out of digits again and so we use yet another column - the "100's" column to get 000100. Our odometer now informs us that we've driven "ONE set of a HUNDRED miles".
So, If we drive 352 miles, the odometer above says we’ve actually driven THREE sets of a HUNDRED miles, FIVE sets of TEN miles and 2 additional miles.
In the Binary (Base 2) number system, there are only two digits available 0,1, so instead of working in sets of 10, we work in sets of 2. That means each column represents a number that is the double of the one to the right of it. The table below may help
| Binary |
128s |
64s |
32s |
16s |
8s |
4s |
2s |
1s |
|
The rules for counting in Binary are the same as decimal - start at zero, count up until you run out of digits, then start a new column. Now, how does this work with only two digits?
Imagine the car with a BINARY odometer. As the car has NO miles, the odometer reads 000000. Just like decimal, the binary odometer tells us we have ZERO miles on the car.
If we drive 1 mile, the clock will read 000001 because just like with decimal, we increase the last digit by 1. But when we drive a second mile, in binary, there is no number 2 - we're limited to 0 and 1 so what do we write?
We have to do what we did when we ran out of digits in Base 10 (Decimal) and create a new column called the "2s" column
The odometer now will read 000010. This tells us "you've driven ONE set of TWO miles".
It might help to compare the two odometers: The decimal Odometer will display 000002 which confirms we've gone "Two Miles" but the Binary Odometer will display 000010. Although this also tells us we've gone 2 miles, it actually reads that we've travelled "ONE set of TWO miles"
Now we drive another mile. The Decimal Odometer would read 000003 which tells us we've gone "Three Miles" but the Binary Odometer reads 000011. This shows us in Binary that we've gone "ONE set of TWO miles, plus one additional mile, totalling 3 in all
So what happens when we drive another mile? How do we show 4 miles on the clock?
Because we are working in "sets of two" we need another column (the 4’s column) to show TWO sets of TWO. The odometer would show 000100 or "one set of Four Miles" with no additional miles.
It becomes quite easy to continue. So, lets continue to drive.. At Five Miles the Binary odometer would show - 000101 -or "One set of Four miles, plus One mile". At Six miles it would read 000110 - "One set of Four miles, plus One set of Two miles"
Now, if we were to drive 23 miles, how would we write that in binary? We would need to work out how many binary sets there are in the decimal number and then represent that in the relevant columns by 1s and 0s.
| Binary |
128s |
64s |
32s |
16s |
8s |
4s |
2s |
1s |
|
0 |
0 |
0 |
1 |
0 |
1 |
1 |
1 |
Twenty three would be represented as 00010111 or “One set of sixteen miles, One set of four miles, one set of two miles and I additional mile”
Binary numbers are used by computer programmers to represent every number, letter and key stroke on a computer in a universally understood and agreed form. Using binary code is the beginning of how computer programmes are developed. The numbers are normally grouped in series of 8 digits. Using this approach, you can translate any binary number into decimal, although there can be a huge string of 1s and 0s for really large numbers. There are lots of binary converters on the internet but hopefully you will be able to convert these numbers without help
And now for the puzzle. In order to make things easier, we have treated each grouping of digits in the coordinates as separate numbers. You need to translate the following binary numbers to get the decimal digits that make up the co-ords
North
00110110
00110111
11001001
West
00000010
00111001
0110110101
You can check your answers for this puzzle on GeoChecker.com.
Now, that wasn't so bad was it? Now you have solved the puzzle you can enjoy a walk to the final cache site, collecting our other caches along the way. The cache is a small lock and lock with a few bits inside. The area is suitable for families or anyone who enjoys a walk in the woods although wellies may be needed when wet. It isn't suitable for wheelchairs and buggys as it is off the main paths (although an all terrain pushchair would probably be ok). As it's a popular dog walking area, beware of muggles and remember that a bit of CITO is always welcome as people do leave litter.
The area is a richly diverse woodland with oak and beech trees,ponds hedgerows and open fields and is home to a great variety of birds, insects and small mammals. There are numerous trails through the woods with convenient benches and seats and it is possible to follow the course of the old Carlisle Bells race track. Thanks to Carlisle City Council Countryside Section who have allowed all the Kingmoor caches to be placed.
It is possible to visit this and three of our our other caches on a circular walk.
GC1C98N Kingmoor - The Carlisle Bells
GC1PW1D Kingmoor - The Rookery
GC1P962 Kingmoor - Stringing You Along
Parking is at N 54 54.686 W 002 57.369