Number formation problems involve creating numbers with specific digit constraints. Systematic approach: (1) identify the most constrained position and fill it first, (2) apply multiplication principle for remaining positions. For an n-digit number: the first digit cannot be 0 (unless leading zeros are allowed). Divisibility constraints determine the last digits: divisible by 2 (even last digit), by 5 (last digit 0 or 5), by 4 (last two digits divisible by 4). When repetition is not allowed, each position reduces available digits by one. When repetition is allowed, each position has the same count. JEE variations: "how many numbers between 100 and 999 have exactly one repeated digit" or "how many 5-digit numbers formed from {0,1,2,3,4,5} are divisible by 3." Sum of all such numbers is another variant — compute digit contribution at each position.
Part of ALG-07 — Permutations & Combinations
Digit and Number Formation Problems
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