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## Doors and Numbers

A cache by ThomasLinge Message this owner
Hidden : 12/12/2009
Difficulty:
Terrain:

Size:  (small)

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### Geocache Description:

The above coordinates are simply: WRONG

In a small school, there are exactly ninety-nine students and ninety-nine lockers.

The mathematics teacher asks the students to help him with a number theory experiment and do the following:

Student number 1 will run through the school and open every locker door.

Student 2 will run through and close every second door (i.e. door 2, 4, 6, 8,…).
Student 3 will run through and reverse every third locker door beginning with (3, 6, 9, 12, …)
in such a way that if the door is open Student 3 will close it and if the door is closed Student 3 will open it.
Student 4 will reverse every fourth locker door (4, 8, 12, 16, …) and so on.
When all ninety-nine students have done their job, which lockers remain open? What numbers are on the open doors?

Add the numbers on the open doors and then add the 83rd magic prime number. Use the result in one of the coordinates.

Consider the following Limerick:

Fifty-two is the sum of two squares:

And three less is a square! So who cares?

You may think it is curious,

Perhaps it is spurious,

Are there other such numbers somewheres?

Find the largest such number that can be written with only three

digits and take away the magic number 684 which has many

hidden secrets. The result is suitable in the other coordinate.

The cache is at N 57 39.NNN E 011.54.EEE

The cache consist of a 350 ml Lock & Lock, and it contained from the beginning pencils, log book, some golf tees, a golf ball, and a Euro coin. Good Luck!!!

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