PS3.md

Basic Math & Number Theory Problems

These problems are solved by applying properties of numbers like divisibility, prime factors, and parity.

• Sum of Round Numbers (1352A)
  Rating: 800
  Topic: Digit Decomposition

  Hint

  Use modulo and division to extract each digit and its place value.

• Balanced Array (1343B)
  Rating: 900
  Topic: Parity, Construction

  Hint

  Construct the array with even and odd numbers to balance sums.

• Multiply by 2, divide by 6 (1374B)
  Rating: 1000
  Topic: Prime Factorization

  Hint

  Only prime factors 2 and 3 involved. Check counts of 2s vs 3s.

• Phoenix and Balance (1348A)
  Rating: 900
  Topic: Math, Powers of 2

  Hint

  Place 2^n coin in one pile, distribute remaining coins optimally.

• Same Differences (1520D)
  Rating: 1300
  Topic: Algebra, Counting

  Hint

  Rearrange equation and count frequencies of `a[k] - k`.