Why Number Sequences?
Number sequences create satisfying "aha!" moments when solvers recognise the pattern. They're ideal for:
- Math enthusiasts — Appeals to cachers who enjoy logical puzzles
- Themed caches — Perfect for educational or science-themed hides
- Variable difficulty — From obvious Fibonacci to obscure sequences
- Self-verifying — Solvers can check if their answer fits the pattern
Common Sequences for Puzzles
Fibonacci Sequence
Each number is the sum of the two preceding ones.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...
Prime Numbers
Numbers divisible only by 1 and themselves.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31...
Triangular Numbers
Sum of first n natural numbers.
1, 3, 6, 10, 15, 21, 28, 36, 45, 55...
Square Numbers
n squared.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
Happy Numbers
Sum of squares of digits eventually reaches 1.
1, 7, 10, 13, 19, 23, 28, 31, 32, 44...
Method 1: Sequence Position Encoding
Use positions in a sequence to represent coordinate digits:
Target coordinates:
N 51° 23.456
Prime number encoding (digits = position of prime):
5=3rd prime, 1=1st prime (sort of), 2=1st prime, 3=2nd prime...
Present it as: "Find the 3rd, 1st, 1st, 2nd, 2nd, 4th, 3rd, 6th primes"
Tip: Use our Number Sequence Solver to generate and verify sequences.
Method 2: Find the Missing Number
Present a sequence with blanks that solvers must fill in:
Puzzle presentation:
N 51° 2_.___
Fibonacci: 1, 1, 2, _, 5, 8, 13, 21, _, 55
The missing numbers (3, 34) give you: N 51° 23.345
This method works well because solvers must understand the sequence to fill in the gaps.
Method 3: Sequence Operations
Use arithmetic operations on sequence values:
"The latitude minutes are the 7th Fibonacci number minus the 4th prime."
- 7th Fibonacci = 13
- 4th prime = 7
- 13 - 7 = 6
This approach lets you hit specific coordinate values that might not appear directly in sequences.
Step-by-Step Creation Process
1. Choose Your Target Coordinates
Start with your cache location. Note each digit you need to encode.
2. Select Appropriate Sequences
Match sequences to your theme. A nature cache might use Fibonacci (found in nature). A space-themed cache could use distances to planets.
3. Map Digits to Sequence Values
Decide how each coordinate digit will be derived. Consider using multiple sequences for variety.
4. Create Clear Instructions
Write unambiguous instructions. "The 5th prime" is clear. "A prime around 10" is not.
5. Add Thematic Context
Weave the math into a story. "The mathematician left 8 clues, each related to his favourite sequence..."
Complete Example Puzzle
Cache Title: "Nature's Numbers"
Cache description:
"The spiral of a nautilus shell, the petals on a flower, the branches of a tree—all follow the same ancient pattern discovered by Leonardo of Pisa."
To find the cache:
N 5A° BC.DEF
W 00G° HI.JKL
A = 1st number in the sequence
B = 4th number
C = 6th number
D = Position where 21 appears
E = Sum of 1st and 2nd numbers
F = 5th number
G = 2nd number
H = 3rd number
I = Position where 8 appears
J = 7th number minus 3rd number
K = 1st number
L = 4th number
Solution:
Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34...
A=1, B=3, C=8, D=8, E=2, F=5, G=1, H=2, I=6, J=11, K=1, L=3
N 51° 38.825, W 001° 26.113
Difficulty Variations
Easy (D1.5-D2)
- Use well-known sequences (Fibonacci, primes)
- Name the sequence explicitly
- Provide the first few numbers
Medium (D2.5-D3)
- Don't name the sequence, let solvers identify it
- Use less common sequences (triangular, Lucas)
- Require arithmetic operations
Hard (D3.5+)
- Use obscure sequences or create custom ones
- Combine multiple sequences
- Require sequence identification from partial data
Pro Tips
- Reference OEIS. The Online Encyclopedia of Integer Sequences (oeis.org) is a goldmine for sequence ideas.
- Be consistent with indexing. Clearly state if you count from 0 or 1. "The 1st Fibonacci is 1" vs "F(1) = 1".
- Test your math. Double-check all calculations. One wrong number ruins the entire puzzle.
- Provide a check digit. Include a way for solvers to verify their work, like "all coordinate digits sum to 42".