math plus enumeration Pattern
12 problems
Pattern pages help build reusable solving frames. Identify signals first, then explain state, transition, and edge handling.
Recognition Signals
- Expect efficient palindrome generation without checking all products.
- Look for correct handling of modulo 1337 to avoid integer overflow.
- Can the candidate quickly recognize the mathematical pattern behind consecutive sums?
Solve Flow
- 1. Define the active state/window.
- 2. Update state while preserving invariants.
- 3. Validate with edge-heavy examples.
Common Misses
- Checking every product of n-digit numbers instead of generating palindrome candidates first.
- Forgetting that the starting number must be positive, which could lead to invalid sequences.
- Failing to account for the fact that (a, b) and (b, a) represent the same triple, leading to double-counting.
Recommended Ladder
Largest Palindrome Product
Find the largest palindromic number from the product of two n-digit integers using math and enumeration efficiently.
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Count Square Sum Triples asks to find the number of integer triples where a² + b² = c² for values between 1 and n.
Three Divisors
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Sum of k-Mirror Numbers
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