Step 1: Collecting
Answer the following questions to build your collection of eleven numbers:
- Whenever Cacher_Roy finds a large enough geocache, he leaves one of his signature items in it. These come in 4 colors. Feeling optimistic, he took 25 of each color on a recent trip. After a few days he counted the ones that he still had, and noticed that exactly one fifth of them were blue. After placing another one in a cache, he realized that exactly one fourth of the remaining ones were red. He dropped off two more, and saw that exactly one third of the ones that he still had were green. How many signature items did he have then?
- How many triangles, of any shape and size, are in the picture below?
- What number is hidden in this picture?
- Alice and Bob were born on the same day of the year, in different years. Today is their birthday, and Alice is 3 years older than Bob was when Alice was three times as old as Bob was when Alice was half as old as she is now. How old (in years) is Alice? (Click here for a hint.)
- What number is hidden below?
The answers to the last five questions can be found within 700 miles of the cache. Two of the places are in the Arcata Forest; if you decide to get these last, be sure to bring paper and a pencil with you to figure out the final coordinates.
- What's the numeric part of the name of the city at N 34° 8.138 W 116° 3.264?
- What two interstate highways meet at N 38° 34.641 W 112° 36.206? (Two numbers from one question.)
- At N 40° 50.881 W 124° 04.072, there's a bench honoring teachers at the Jacoby Creek School. Ironically, it has a misspelled word. How many letters are in that word? (You can park about 300 feet southeast of the bench.)
- There's a sign at N 40° 52.611 W 124° 03.687, which contains two trail numbers. What's 7 times the smaller number?
- There's a plaque at N 40° 52.663 W 124° 03.687; the bottom line has two numbers. What's the product of the last digit of the first number and the last digit of the second number? (There's a picnic table nearby, where you could sit and compute the coordinates.)
You should now have a collection of eleven numbers. As a partial check that you got them right, add them up; the sum should be 448.
Step 2: Discarding
Now it's time to get rid of some numbers.
- First, discard two numbers whose sum is 57. You'll have nine numbers left.
- Next, throw out two numbers whose difference is 23. You'll have seven numbers left.
- Then eliminate two numbers whose product is 420. You'll have five numbers left.
- Finally, omit two numbers whose quotient is 2. You'll have three numbers left.
Step 3: Computing the coordinates
Call the three remaining numbers S, L, and M, where S is the smallest, L is the largest, and M is in between. Let:
- A = tens digit of L
- B = ones digit of L+S
- C = tens digit of L+S
- D = tens digit of M+S
The coordinates of the cache are N 40° 52.ABC W 124° 03.DAB.
If you think you've figured out the coordinates, you can check them with certitude:
You can also see who else has solved the puzzle. Note: You can remain anonymous if you want to; incorrect guesses are always anonymous. (Puzzle makers, you can create your own certitude links here.)
Or you can check your coordinates here: Geochecker.com
Step 4: Finding the cache
The cache is an ammo can. To get the coordinates I averaged several readings, all within 30 feet of the average. Still, this is a forest, and your readings may differ from mine, so the hint should let you make the find once you get close.
Congratulations to Phobos+Demos for FTF! They received an unactivated Datastorm geocoin, courtesy of dbirdman and catlady. (Thanks!)