The cache is not located at the above co-ordinates. There is no need to physically visit there. Please read the cache page thoroughly before attempting to look for this cache.
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Mesdames et Messieurs, sit yourselves down and prepare yourselves for a gastronomic treat of the finest culinary delights.
Our team of chefs have been trained in specialities from all over the world for your caching delectation!
We hope you will find many things that you will enjoy.
BON APPETIT!
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About this Series
Beachies' Bistro is a series of puzzle caches located in and around Peterborough with (if you haven't guessed already) a foodie theme. There are nine courses - see the menu below. Each course has a cache to find. In addition, there is a bonus cache ("The Bill"), which can be found using information located in all of the courses.
The puzzles are not meant to bemuse. We have pitched them with varying difficulties so that hopefully everyone can enjoy as much as possible of this series. The difficulty level, as you might expect, increases as you go through the meal. Some of the later, more difficult, puzzles have clues located in the geocheckers of earlier caches in the series; these are to assist you where needed, although all can be solved using the information on the cache page. (with the exception of the bonus, because the relevant information is contained within the caches in the series)
We have designed the series such that you can work out the puzzle elements at home before you leave (with the exception of the bonus), and pick up all of the physical caches in one day. Or you can do it in bite-size portions, it's up to you!
We would ask however that you do not leave any spoilers in your logs, even encrypted, including pictures. Please don't spoil the meal for future cachers!!
Please take either a notebook & pen or a camera phone with you so that you can take a record of the bonus information written in the caches.
The Main Course
For main we have Roast PARTRIDGE.
The Puzzle: "Partridge Puzzles"
The Partridge Puzzle was devised by a Mathematician named Robert Wainwright. He started with the below mathematical identity:
Put in another way, if you take any given integer n, if you take all of the integers from 1 to that number inclusive, cube them all, and add the cubes together, the sum total is equal to the square of the sum of all of the numbers from 1 to n. For example, if you choose n = 3, then:
It can be proved by induction that this identity is true for all values of n greater than or equal to 1.
Taking this to a vaguely practical level, imagine a 3 x 3 x 3 cube. You can, if you wish, divide this into three 3 x 3 x 1 cuboids, and do the same with a 2 x 2 x 2 cube, dividing it into two 2 x 2 x 1 cuboids, and of course a 1 x 1 x 1 cube is already one 1 x 1 x 1 cuboid. These six cuboids combined will, according to the identity, take up the same number of space as a 6 x 6 x 1 cuboid. (imagine the smaller pieces as jigsaw pieces put together to make 6 x 6 jigsaw, where all of the pieces are 1 unit thick)
Now in the example given, the jigsaw doesn’t work, you can’t make a 6 x 6 x 1 cuboid out of three 3 x 3 x 1s, two 2 x 2 x 1s, and a 1 x 1 x 1. But Wainwright presented the problem: what is the smallest value of n such that the jigsaw will work?
Other mathematicians took on this problem and one called Bill Cutler found what is thought to be the lowest, a solution based on n = 8, or to put it another way, a 36 x 36 square filled with eight 8 x 8 squares, seven 7 x 7 squares, and so on down to one 1 x 1 square. (36 = 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) You can work out for yourself how this relates to the identity above or take it from us that it does. The solution is below:
As 8 is the lowest known value such that the jigsaw will work, 8 is said to be the Partridge number for squares.
Now other mathematicians took this research further and set about working out Partridge numbers for other shapes. From the below diagrams, it can be determined that the partridge numbers of the below shapes are 9, 8, 5, and 4 respectively.
But let us revisit the square again. The aforementioned Bill Cutler found that there are 2,332 different ways to make the jigsaw using the pieces below.
Mr Beach_hut wrote the co-ordinates of this cache down in the form of a QR code. He then chose one of the 2,332 arrangements, divided the QR code into a jigsaw using that arrangement, and broke it in its constituent pieces, leaving you, the intrepid puzzle solver, to work out which of the 2332 arrangements we chose, and then reassemble the jigsaw, read the QR code, and identify the co-ordinates to the cache. What could be simpler??!
However, in a freak accident, the pieces of Mr BH’s QR code jigsaw were tragically shredded, burnt and eaten, just for good measure. A disgruntled puzzle solver is suspected…
This means the QR code jigsaw will never see the light of day. I’m sure you’ll agree that’s a spot of awful luck.
In place of the advertised puzzle, here are some pictures.
(Yes, all of that mathematical discussion was just a load of pre-amble. But at least you’ve learned something, and give yourselves a pat on the back if you read this far down the page!)
Finding this cache
Work out the numerical value associated with each picture, and then you just need to plug the numbers into this equation to find the cache:
N 52° (A-C)(C+F).(H-F)(G-H)(B+E-H) W 000° F(D-E).(B-A-F)(A-E)A
"Tasting notes"
Parking is available a short walk from the cache site. Above all, please park considerately, safely and legally.
The final cache site is not suitable for wheelchair users I'm afraid.
Stealth will be required at final location at many times. If you get to GZ and find the scene busy, please leave for another time.
Please do not look for this cache during the hours of darkness.
Please bring your own pen.
And finally, the "check"...
