DOG POUND Mystery Cache
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Difficulty:
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Terrain:
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Size: 
(micro)
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The coordinates are not exactly those of the cache. They are for the gate to the old Pepperell dog pound on Heald Street in Pepperell MA which is where the cache is hidden.
On the picture (see below) of the old Pepperell dog pound, there are ten possible hiding spots for the cache numbered from 1 to 10. You will need to apply some simple math concepts to determine which one is correct from the following clues, some of which are purposely irrelevant. This might be a good math challenge for one of your older children.
The product of this number and its reciprocal is one.
You cannot divide this number by zero.
It is not a prime number.
If you squared this number, and then squared the new number, your ones digit would be six.
The square root of this number is an irrational number.
The prime factors of this number are all less than five.
If you multiply the correct number by the multiplicative identity you will get a number that would also be considered correct.
This number is less than the digit in the 100 billionths decimal place of pi.
PLEASE NOTE: The cache container is small and matches its surroundings. It contains only a logbook. There are no trade items and no writing instrument - you must supply your own. The container had to be “engineered” a bit to make it close tightly. As a result you may have to exert a bit of pressure to open it - but it will open! Please close carefully and replace it EXACTLY as you found it.
Additional Hints
(Decrypt)
[No hints at this time.]