CC37 Cannon Balls – a Likely Story
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(regular)
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This is the thirty-seventh of a series, the “Caerphilly Collection”, that will explore the whole Borough Council area. The cache, a medium size plastic lunch box, is hidden within 6 miles of the reference location, but its position, at a distinctive man-made landscape feature, has to be derived from a mathematical puzzle, linked to a piece of history (allegedly!). Be prepared to walk up to 2 miles with 350feet of ascent, but finding a way to the cache is part of the puzzle.
The Caerphilly Collection is distinguished with a unique CC number and is made up of 50 caches. The caches vary in difficulty and type and usually have other “C” word connections – castle, cheese, coal, canal, etc. There may even be Cryptic Clues for Clever Clogs! The current Caerphilly unitary authority grew out of the former Rhymney Valley and Islwyn Councils and stretches from the outskirts of Cardiff and Newport in the south to the Brecon Beacons, north of Rhymney. Despite a past dominated by coal and heavy industry, it has a diverse history and varied and dramatic scenery. We hope you will enjoy exploring it with us.
Towards the end of the Collection is CC48 The Accumulator, the location of which is given in coded form. The translation details of the code are distributed around the whole Collection, but only about a third of the caches will contain a piece of the code, which is on the back of the Log Book. To do the Accumulator, you will need to keep a note of each piece of code that you find. Unless you are very lucky, you will need to find the majority of the Collection in order to do the Accumulator. The Accumulator cache is hidden in an area of difficult terrain and demanding navigation, with a 5,4½ rating.
This cache is hidden near a landscape feature that was new to us, but which caught our attention while planning earlier caches in the series - so we had to go looking for it (CC standing for cachers’ curiosity).
To find the cache coordinates, you need to solve the following problem.
You have a number of cannon balls arranged in a triangle (like the red balls in snooker). You then arrange the balls in a square-based pyramid such that none are left over. What is the least number of cannon balls that you could have?
(The answer one is not acceptable.)
Too easy? Well, can you find another solution?
Still too easy? Okay, can you find a third solution?
Write down the three solutions in sequence, which will give you a string of 10 numbers, represented by the letter sequence:
a a b c d e f g g a
The cache is located at: N 51 gf.dhd W 003 ce.bjb, where h = a + c and j = b - d
If you want to impress your friends, you could derive a fourth solution … but it is a rather long number.
The reference location for this cache is indicative of the general area only, but could, perhaps, be a parking location. Although the cache is close to a public right of way and not far from the nearest road, it is difficult to find convenient/considerate parking spots in the narrow lanes nearby. You will have to plan your approach with this in mind. The public right of way to the cache is designated as a “road used as a public footpath” – the reality belies this description. Note also that it is completely obstructed just north-east of the cache location (so don’t attempt to approach from the north). Bearing these points in mind, part of the puzzle is working out how to get to the cache, using public footpaths and roads. A good map is essential.
PLEASE NOTE THAT THE CACHE LOCATION DOES NOT REQUIRE YOU TO GO RIGHT UP TO THE VERTICAL ROCKFACES IN THE VICINITY, WHICH MAY BE UNSTABLE.
PUZZLE POSTSCRIPT: The cannon ball problem was first posed in Henry VIII’s time. Finding the third solution was taxing the admirals and senior officers of the fleet until, one day, the captain of a ship moored in the Solent sent messages to all other ships in the area that he had the answer. No one believed him, so he invited them all to his ship, bringing their stock of cannon balls with them. The ship was the Mary Rose … and the rest, as they say, is history. This was one of the king’s favourite ships and many admirals were implicated in its loss. Also, the news of this “own goal” had to be kept from the French, with whom we were at war. The result was a mammoth cover up – which is why you won’t find this story in history books.
Additional Hints
(No hints available.)