Check 9: need two multiples of 3, but in five consecutive, only one multiple of 3 unless spaced correctly (e.g., 3 and 6: 6 is divisible by 3, 3 by 3 → only one multiple of 3 unless 9 appears). Sequence 7–11: none divisible by 3 → product not divisible by 3? Wait: 9 is divisible by 3, but if no multiple of 3, like 4–8: no multiple of 3 → product \( 4 \times 5 \times 6 \times 7 \times 8 \)? Wait, 6 is included → divisible by 3.

Sun, 03 May 2026 15:02:22 +0000

# Understanding Check 9: Multiples of 3 in Consecutive Sequences In mathematics and number puzzles, Check 9 is a concept centered around divisibility rules—particularly the powerful property that a number is divisible by 3 if the sum of its digits is divisible by 3. But more recently, a specific criterion has emerged: in any set of five consecutive integers, there’s a unique multiple of 3—except when multiples cluster unnaturally, such as in sequences containing both 3 and 6, or gaps like 4–8 where no multiple of 3 appears. This article explores the precise rule behind Check 9, why five consecutive numbers typically contain exactly one (or potentially two) multiple of 3—but only when spaced correctly (e.g., 3 and 6, or 9 appearing)—and why sequences like 4–8 (with no multiple of 3) break the pattern. Whether you're solving number puzzles or understanding divisibility deeply, mastering this rule is essential. ---