NEURAL NETWORK CHALLENGE v8.8.8

Level 2: Neural Pattern Recognition

Complete the pattern matrix:

2  5  10  17
4  9  16  25
8  15 24  35
16 23 ?  47
      

Level 3: Quantum Entanglement Cipher

Decrypt the following quantum state equation:

|ψ⟩ = α|0⟩ + β|1⟩, where:

α² + β² = 1

If α = 0.6, calculate β to maintain quantum coherence

Level 4: AI Neural Pathway Optimization

Given a neural network with weights:

[0.3  0.5  0.8]
[0.4  0.7  ?  ]
[0.2  0.6  0.9]
      

Calculate the missing weight to maximize network efficiency using the golden ratio (φ)

Level 5: Cryptographic Hash Sequence

Complete the hash sequence based on prime factorization:

2¹ × 3² = 18

2² × 3¹ = 12

2³ × 3⁰ = 8

2⁴ × 3? = 48

Level 6: Quantum Superposition Matrix

Given the following quantum state transitions:

|ψ₁⟩ → |ψ₂⟩: +3i
|ψ₂⟩ → |ψ₃⟩: -2 + i
|ψ₃⟩ → |ψ₄⟩: 4 - 2i
|ψ₄⟩ → |ψ₅⟩: ?
      

Calculate the final transition value to maintain complex unity.

Level 7: Recursive Neural Entropy

Analyze the recursive pattern:

f(1) = 1
f(2) = f(1) + 3 = 4
f(3) = f(2) + f(1) + 5 = 10
f(4) = f(3) + f(2) + f(1) + 7 = ?
      

Level 8: Hyperdimensional Vector Analysis

In a 4D hypercube, calculate the missing coordinate:

Point A: (2, 4, 6, 8)

Point B: (3, 6, 9, 12)

Point C: (4, 8, 12, 16)

Find the value for the unknown coordinate: (5, 10, ?, 20)

Level 9: Neural Network Frequency Analysis

Given the following signals:

Signal A: 4Hz, Signal B: 8Hz, Signal C: 12Hz

What is the dominant frequency of the combined signal?

Level 10: Ultimate Neural Encryption

Decode the encrypted message:

”Evhf!Ivnz!Puvm!”

Apply the Caesar cipher with a shift of 7.