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Sidetracked: Timetables vs Times tables? Mystery Cache

This cache has been archived.

Taxi1729: I am archiving this geocache because of issues with its current location. It will shortly be resuscitated at a location a short distance away.

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Hidden : 4/14/2015
Difficulty:
2 out of 5
Terrain:
1.5 out of 5

Size: Size:   micro (micro)

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Geocache Description:


The cache is a small magnetic container, about the size of a small marble. You will need to bring your own pen/pencil/quill. It is not at the given coordinates, but is within 2.5 km of that position.

The coordinates are calculated by solving a short Maths quiz. Fear not! There is no need to spend 3 years studying at university. Indeed, with this quiz, it will take only 60 minutes to get a degree. By approaching the cache from the right angle, I hope you will soon have it in hand and be able to sine the log. Why not tackle it with a friend? - then you'll be able to cosine. I have tried to integrate the cache with its surroundings, but I hope geocachers will have no problem differentiating the two, allowing them to maintain their logger rhythm. The puzzle is not complex; to solve it, you just need to keep a real, positive attitude. However, keep (1, i) open for muggles – this is a popular area for walkers.

Please note that the cache is accessible from the path - there is no need to climb on or through anything.

The cache is accessible by wheelchair, but there is a potential impediment if you approach from the South. If this proves impassable, there is access from the North (but to reach this, you may need to take quite a detour - a square route).

A logbook in a Really Sidetracked cache… surely that must be a Stationery Point?

But I'm going off on a tangent, let's get back to the Quiz.

In tackling these questions, it may help to know that the first two questions involve my two favourite fractions, one of which is 1/81 and that the third relates to my favourite mathematical story which involves a brilliant mathematician who was born in 1887.

1. What are the 3 next numbers in this sequence?   0,1,2,3,4,5,6,A,B,C,...

The sequence continues, but you can ignore everything after the C.

2. At school, we learn that 22/7 is a good approximation to π. However, there is a much nicer one and it inspired this part of the question.

What is the nearest whole number to 113 x π ? Answer = DEF.

(Thus, a very good approximation to π is DEF/113 and it’s accurate to 7 digits.)

3. The number 133 can be written as the sum of two positive cubes: 133 = 125 + 8 = 53 + 23, but what is the smallest positive integer than can be written as the sum of two positive cubes in two different ways? Answer = GHJK

The cache is located at N 51° ED.J(H-G)C    W 002° (K-B)A.(E-G)F(D+J)

You can check your answers for this puzzle on GeoChecker.com.

Congratulations to Elliott150 on the FTF.

Additional Hints (Decrypt)

D1: gel jevgvat 1/81 nf n qrpvzny D3: Gur zngurzngvpvna jnf pnyyrq Enznahwna Svany ybpngvba: Nccebk 1.5z Uvtu Cbg va Hfr. Abg ba envyvat.

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)