372, 823, 644, 582, 46?, 8?7. Then which digits will come at the place of (?)
2023
372, 823, 644, 582, 46?, 8?7. Then which digits will come at the place of (?)
Answer: C. 6,2 — Concept In a number-series puzzle where the terms themselves don't show an obvious pattern, check a derived quantity instead — here, the sum of the three…
- A.
6,7
- B.
5,9
- C.
6,2
- D.
5,3
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Concept
In a number-series puzzle where the terms themselves don't show an obvious pattern, check a derived quantity instead — here, the sum of the three digits of each term. When these digit-sums increase by a fixed amount from term to term, a missing digit is found by first fixing the target digit-sum for its own term from that pattern, then solving the simple digit equation.
Application
Compute the digit-sum of each fully known term: 372 → 3+7+2 = 12; 823 → 8+2+3 = 13; 644 → 6+4+4 = 14; 582 → 5+8+2 = 15.
These digit-sums form an increasing sequence with common difference 1: 12, 13, 14, 15, …
Extending the sequence, the fifth term 46? must have digit-sum 16, and the sixth term 8?7 must have digit-sum 17.
Solve each digit equation: for 46?, 4 + 6 + ? = 16, so ? = 6; for 8?7, 8 + ? + 7 = 17, so ? = 2.
The missing digits are 6 and 2 respectively, i.e. the pair "6,2".
Cross-check
Substituting back confirms both totals: 4+6+6 = 16 and 8+2+7 = 17, continuing the unbroken +1 progression 12 → 13 → 14 → 15 → 16 → 17, so the pair (6, 2) is fully consistent with the pattern established by the earlier terms.