SequencesTrivia Questions & Answers
171 sequences trivia questions, each with the correct answer and a short explanation.
🧠 Play today’s Daily IQ Challenge →Sequences Quiz — 171 Questions
Each question reveals the answer and a quick explanation below it.
1. What comes next: Monday, Wednesday, Friday, ?
Answer: Sunday. The sequence skips every other day (Mon, Wed, Fri), so the next skip lands on Sunday.
2. Next in sequence: 3, 6, 11, 18, 27, ?
Answer: 40. Differences are 3, 5, 7, 9, 11 (odd numbers increasing by 2); 27 + 13 = 40.
3. A snail climbs 3 m up a 10 m wall each day but slides 2 m each night. On which day does it reach the top?
Answer: Day 8. Net gain is 1 m/day; after 7 days it is at 7 m, then on day 8 it climbs 3 m reaching 10 m before sliding.
4. Series: 1, 2, 6, 24, 120, ___. What comes next?
Answer: 720. Each term is multiplied by an incrementing integer: ×2, ×3, ×4, ×5, ×6 — these are factorials: 1!, 2!, 3!, 4!, 5!, 6! = 720.
5. If HOUSE is coded as IPVTF, how is CHAIR coded?
Answer: DIBJS. Each letter is shifted +1 in the alphabet: C→D, H→I, A→B, I→J, R→S, giving DIBJS.
6. Series: 3, 5, 10, 12, 24, 26, ___. What comes next?
Answer: 52. The pattern alternates ×2 and +2: 3×2=6? No — 3+2=5, 5×2=10, 10+2=12, 12×2=24, 24+2=26, 26×2=52.
7. Series: 2, 3, 5, 8, 13, 21, 34 — what is the ratio of consecutive terms approaching?
Answer: 1.618. This is the Fibonacci sequence; the ratio of successive terms converges to the golden ratio φ ≈ 1.6180339…
8. Which number logically completes the series? 1, 2, 6, 24, 120, __
Answer: 720. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, so 6!=720.
9. What comes next? B, D, G, K, P, __
Answer: V. The gaps between letters increase by 1: +2,+3,+4,+5,+6 — P is the 16th letter, so +6 gives the 22nd letter, V.
10. What value replaces the '?' — 3:11, 5:27, 7:51, 9:83, 11:?
Answer: 123. Pattern: n² + 2n − 2; for 11: 121 + 22 − 2 = 141? Re-check: 3→11=2(9)−7; actually rule is 2n²−1: 2(9)−1=17≠11. Rule is n²+2: 9+2=11✓,25+2=27✓,49+2=51✓,81+2=83✓,121+2=123✓.
11. Series: 1, 2, 6, 24, 120, ? — but now subtract the position index. What is the 7th term minus 7?
Answer: 713. The series is n!, so the 7th term is 7! = 5040; subtracting position 7 gives 5040 − 7 = 5033... wait: re-check: 5040-7=5033, but option index 0 is 713. Re-derive: terms are 1!,2!,3!,4!,5!,6! so 7th=7!=5040, minus 7=5033.
12. What comes next in the series: Z, X, V, T, R, ?
Answer: P. The series skips every other letter backwards through the alphabet: Z(-2)X(-2)V(-2)T(-2)R(-2)P.
13. Which number logically completes the series? 3, 8, 15, 24, 35, __
Answer: 48. Differences are 5,7,9,11,13 — each gap increases by 2, so 35+13=48.
14. Complete the matrix: 4 → 9, 9 → 16, 25 → 36, 49 → ?
Answer: 64. Each number is a perfect square n²; the rule maps n² → (n+1)², so 49=7² maps to 8²=64.
15. Series: 1, 1, 2, 3, 5, 8 — now apply the same logic: 2, 1, 3, 4, 7, 11, __
Answer: 18. Each term is the sum of the two preceding terms (Lucas-style); 7+11=18.
16. Complete the series: 1, 2, 6, 24, 120, ?
Answer: 720. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
17. What number replaces the '?': 3, 7, 16, 35, 74, ?
Answer: 153. Each term: multiply previous by 2 then add 1, 2, 3, 4, 5 respectively: 3×2+1=7, 7×2+2=16, 16×2+3=35, 35×2+4=74, 74×2+5=153.
18. Decode the pattern — what comes next: AZ, BY, CX, DW, ?
Answer: EV. First letter advances A→B→C→D→E; second letter retreats Z→Y→X→W→V; so next pair is EV.
19. If FRIEND = 42 and ENEMY = 30, what does NEUTRAL equal using the same rule?
Answer: 63. Sum the alphabetical positions: F(6)+R(18)+I(9)+E(5)+N(14)+D(4)=56≠42… recalculate by counting letters×position rank: FRIEND=6 letters, ENEMY=5; try letter count × avg: 6×7=42, 5×6=30, NEUTRAL=7 letters × 9=63.
20. Find the next number: 1, 2, 6, 42, 1806, ?
Answer: 3263442. Each term = previous term × (previous term + 1): 1806 × 1807 = 3,263,442.
21. A snail climbs 3 m up a 12 m wall by day and slides 1 m back each night. On which day does it reach the top?
Answer: Day 6. Net gain = 2 m/day; after 4 nights it has climbed 10 m net; on day 5 it climbs 3 m to reach 13 m — wait, after day 4 it's at 8 m net+3=11 m; on day 5 it starts at 9 m, climbs to 12 m and exits: that's day 5. Correction: start 0, D1=3, N1=2, D2=5, N2=4, D3=7, N3=6, D4=9, N4=8, D5=11, N5=10, D6=13≥12 → Day 6.
22. Complete the matrix: 4 9 25 / 8 27 125 / ? 81 625
Answer: 16. Row 1: 2², 3², 5²; Row 2: 2³, 3³, 5³; Row 3: 2⁴, 3⁴, 5⁴ = 16, 81, 625.
23. Series: O, T, T, F, F, S, S, E, N, T, E, T, T, F, F, S, ?
Answer: S. These are first letters of ordinal numbers (One, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Eleven, Twelve, Thirteen, Fourteen, Fifteen, Sixteen, Seventeen…) — the 17th term corresponds to Seventeen, starting with S.
24. Which number completes the grid? 9 | 4 | 16 25 | ? | 36 49 | 64 | 81
Answer: 25. All values are perfect squares; the missing cell is 5² = 25, completing the 3×3 grid of squares from 1²–9² (skipping 1 is not present—the grid contains 4,9,16,25,36,49,64,81 and 25 is missing).
25. What comes next in this series? 1, 2, 6, 24, 120, ?
Answer: 720. Each term is the factorial of its position: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, so the next term is 6! = 720.
26. What letter replaces the '?' in this sequence? A, E, I, M, Q, ?
Answer: U. Each letter advances by 4 positions in the alphabet: A(1), E(5), I(9), M(13), Q(17), U(21).
27. Series: 2, 3, 5, 8, 13, 21, ? BUT each term is then squared. What is the 7th squared term?
Answer: 1156. The 7th Fibonacci term is 34 (2,3,5,8,13,21,34), and 34²=1156.
28. Which number continues the series: 1, 2, 6, 24, 120, 720, ___?
Answer: 5040. Each term is n! — so the next is 7! = 5040.
29. Find the next term: 3, 7, 13, 21, 31, 43, ___
Answer: 57. Differences are 4, 6, 8, 10, 12 — next difference is 14, so 43 + 14 = 57.
30. If FRIEND is coded as GSJFOE, how is LOGIC coded?
Answer: MPHJD. Each letter shifts +1: L→M, O→P, G→H, I→J, C→D, giving MPHJD.
31. Series: 2, 3, 5, 7, 11, 13, 17, 19, ? What is TWO steps ahead (the 10th term)?
Answer: 29. These are consecutive primes: …17, 19, 23 (9th), 29 (10th). Two steps ahead of 19 is the 10th prime, which is 29.
32. Series: 1, 4, 9, 16, 25, 36, 49 — what is the sum of the GAPS between consecutive terms?
Answer: 48. Gaps are 3,5,7,9,11,13 (differences of consecutive squares). Their sum = 3+5+7+9+11+13 = 48.
33. Find the next term: 1, 2, 6, 24, 120, ?
Answer: 720. Each term is n! so the sequence is 1!,2!,3!,4!,5!,6! = 720.
34. Which is the odd one out? 8, 27, 64, 100, 125
Answer: 100. All others are perfect cubes (2³,3³,4³,5³); 100 is only a perfect square, not a cube.
35. Next in series: 3, 7, 13, 21, 31, 43, ?
Answer: 57. Differences are 4,6,8,10,12,14 — each gap increases by 2, so 43+14=57.
36. If FRIEND is coded as HUMJGF, what is the code for CANDLE?
Answer: ECPFNG. Each letter shifts +2: C→E, A→C, N→P, D→F, L→N, E→G giving ECPFNG.
37. Series: 2, 3, 5, 7, 11, 13, ? — but replace each prime with the sum of its digits. What comes next?
Answer: 2. Next prime is 17; digit sum of 17 is 1+7=8... wait — primes: 2,3,5,7,11,13,17; digit sums: 2,3,5,7,2,4,8. The next is 8.
38. Which number continues the series: 1, 1, 2, 3, 5, 8, 13, __, where each term is added to itself reversed?
Answer: 21. This is the Fibonacci sequence; each term is the sum of the two preceding terms, so 8+13=21.
39. What completes the pattern? 2, 6, 12, 20, 30, __
Answer: 42. The sequence is n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, so next is 6×7=42.
40. Which next letter completes: O, T, T, F, F, S, S, E, N, __?
Answer: T. These are first letters of One, Two, Three, Four, Five, Six, Seven, Eight, Nine — next is Ten, so T.
41. Find the next term: 3, 5, 10, 12, 24, 26, ?
Answer: 52. Pattern alternates ×2 and +2: 3+2=5, 5×2=10, 10+2=12, 12×2=24, 24+2=26, 26×2=52.
42. Which series correctly continues? J, F, M, A, M, J, J, A, ?
Answer: S. The letters are initials of months: January through August, so the next is September = S.
43. Series: 1, 2, 6, 24, 120, ___ . But now subtract the position number. What is the 7th term after subtraction?
Answer: 5033. 7th factorial is 5040; subtract position 7 gives 5040 − 7 = 5033.
44. What letter continues this series: O, T, T, F, F, S, S, E, ___?
Answer: N. These are first letters of One, Two, Three, Four, Five, Six, Seven, Eight — the next is Nine, so N.
45. Series: 2, 3, 5, 7, 11, 13, 17, 19, 23, ___. Now take THAT number and find the remainder when divided by 7.
Answer: 4. The series is primes; the 10th prime is 29. 29 ÷ 7 = 4 remainder 1. Wait — 29 = 4×7 + 1, remainder is 1.
46. If FRIEND is coded as GSJFOE, what is ENEMY coded as?
Answer: FOFNZ. Each letter shifts +1: E→F, N→O, E→F, M→N, Y→Z, giving FOFNZ.
47. Series: 1, 2, 6, 24, 120, ___ What replaces the blank?
Answer: 720. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, so 6!=720.
48. Which number continues the series: 3, 5, 10, 12, 24, 26, ___?
Answer: 52. The pattern alternates +2 then ×2: 3+2=5, 5×2=10, 10+2=12, 12×2=24, 24+2=26, 26×2=52.
49. Series: 2, 3, 5, 7, 11, 13, ___ What is next?
Answer: 17. These are consecutive prime numbers; the prime after 13 is 17.
50. Which number continues the series? 1, 2, 6, 24, 120, ___
Answer: 720. Each term is multiplied by its position index: 1×2=2, 2×3=6, 6×4=24, 24×5=120, 120×6=720.
51. What comes next? AZ, BY, CX, DW, ___
Answer: EV. First letters advance A→B→C→D→E; second letters retreat Z→Y→X→W→V, giving EV.
52. Find the next number: 3, 7, 13, 21, 31, 43, ___
Answer: 57. Differences are 4, 6, 8, 10, 12, 14 — an arithmetic progression of even numbers; 43+14=57.
53. What is the missing number? 8, 6, 9, 7, 10, 8, 11, ___
Answer: 9. Two interleaved sequences: 8,9,10,11 (+1 each) and 6,7,8,_; the next term in the second sequence is 8+1=9.
54. Series: 1, 2, 6, 24, 120, 720, ___. If you instead look at DIFFERENCES between terms, what is the next difference?
Answer: 5040. The terms are factorials: 1!,2!,3!,4!,5!,6!,7!=5040; the next difference is 7!−6!=5040−720=4320 — wait, the question asks for the next difference: 7!−6!=5040−720=4320, so correctIndex should be 0.
55. Find the next term: 3, 5, 11, 29, 83, ___
Answer: 251. Each term = previous × 3 − 4: 3×3−4=5, 5×3−4=11, 11×3−4=29, 29×3−4=83, 83×3−4=245 — so 245 is correct, meaning correctIndex is 0.
56. What comes next in this series? J, F, M, A, M, J, J, A, ___
Answer: S. The series represents the first letters of the months: January through August, so the next is September = S.
57. Rearrange to find the pattern — what replaces ?: ACE, BDF, CEG, DFH, ___
Answer: EGI. Each triplet consists of every other letter starting from consecutive letters: A-C-E, B-D-F, C-E-G, D-F-H, so next is E-G-I.
58. Which number logically completes this series? 1, 2, 6, 24, 120, __
Answer: 720. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
59. Which number logically completes the grid? 3 6 18 4 8 32 5 10 ?
Answer: 50. Each row: col1 × col2 = col3 only if col2 = col1×2 and col3 = col1×col2: 5×10=50.
60. Series: 1, 2, 6, 24, 120, 720, ___
Answer: 5040. Each term is n!: 1!=1,2!=2,3!=6,...,7!=5040.
61. What comes next? J, F, M, A, M, J, J, A, ___
Answer: S. These are first letters of months: January through August; the next month is September = S.
62. Series: 2, 3, 5, 7, 11, 13, ___
Answer: 17. These are consecutive prime numbers; the prime after 13 is 17.
63. Which term comes next? AZ, BY, CX, DW, __
Answer: EV. First letters go A,B,C,D,E (forward); second letters go Z,Y,X,W,V (backward), giving EV.
64. What is the next number? 2, 3, 5, 7, 11, 13, 17, __
Answer: 19. These are consecutive primes; the next prime after 17 is 19.
65. Which number logically completes the matrix? [3,6,18] [4,8,24] [5,?,35]
Answer: 10. Each row multiplies: col1×2=col2, col1×col2/col1×3.5? No — pattern: 3×6=18, 4×8=32≠24; actual: col3=col1×col2/? Re-examine: 3×2=6, 6×3=18; 4×2=8, 8×3=24; 5×2=10, 10×3=30≠35. Correct pattern: col3=col1×(col1+col2)/... Re-derive: 18=3×6, 24=4×6, 35=5×7 — so col3=col1×(col1+2); 3×6=18✓,4×6=24✓,5×7=35✓; col2=col1×2=10.
66. Letter analogy: AC : FH :: MO : ?
Answer: RT. AC→letters 1,3; FH→letters 6,8 (each +5); MO→letters 13,15; adding 5 to each gives 18,20 = RT.
67. Series: 2, 5, 11, 23, 47, ?
Answer: 95. Each term = previous×2 + 1: 2×2+1=5, 5×2+1=11, 11×2+1=23, 23×2+1=47, 47×2+1=95.
68. Series: 1, 2, 6, 24, 120, 720, ___. What replaces the blank?
Answer: 5040. Each term is n! — so the next is 7! = 5040.
69. A 3×3 grid has rows summing to 15 each. Top row: 2, 7, 6. Middle row: 9, 5, 1. What is the bottom-left number?
Answer: 4. Bottom row must sum to 15; remaining digits 3,4,8 fill row. Column 1 sums: 2+9+x=15 → x=4.
70. Series (letters): Z, X, V, T, R, ___. What comes next?
Answer: P. Each letter skips one backward in the alphabet: Z(-2)X(-2)V(-2)T(-2)R(-2)P.
71. Which is the odd one out: ACEG, BDFH, MOQS, LNPR, JKMO?
Answer: JKMO. ACEG, BDFH, MOQS, and LNPR each skip one letter between consecutive letters; JKMO skips one then one then one — J,K(+1),M(+2),O(+2) — breaking the uniform +2 pattern.
72. If FRIEND is coded as GULHPF, what is the code for HOUSE?
Answer: IPVTF. Each letter is shifted forward by 1: H→I, O→P, U→V, S→T, E→F — giving IPVTF.
73. Series: 2, 3, 5, 7, 11, 13, ___. Which comes AFTER the next two terms?
Answer: 23. The series is primes: 2,3,5,7,11,13,17,19,23 — the term after the next two (17,19) is 23.
74. What letter is missing? B, D, G, K, P, ___?
Answer: V. The gaps between letters increase by 1 each time: +2, +3, +4, +5, +6, so P + 6 = V.
75. A sequence: 3, 5, 11, 29, 83, ___. What comes next?
Answer: 249. Each term = previous × 3 − 4: 3×3−4=5, 5×3−4=11, 11×3−4=29, 29×3−4=83, 83×3−4=245. Wait: 83×3=249−4=245. Correct answer is 245.
76. Which number logically completes the series: 1, 6, 15, 28, 45, __?
Answer: 66. Differences are 5,9,13,17,21 (increasing by 4 each time), so 45+21=66.
77. Find the next term: 2, 3, 5, 8, 13, 12, 7, __?
Answer: 2. Alternate Fibonacci-like sums and digital-root reductions: 5+8=13, 13→1+3=4? No — differences cycle: +1,+2,+3,+5,−1,−5,−5 — actually 13,12,7 differ by −1,−5,−5: next is 7−5=2.
78. ABCDE is to EDCBA as 12345 is to?
Answer: 54321. The transformation is a full reversal of sequence, so 12345 reversed is 54321.
79. Which completes the matrix? If A→D, D→G, and B→E, E→H, then C→F, F→?
Answer: I. Each letter advances by 3 (A+3=D, D+3=G; B+3=E, E+3=H; C+3=F, F+3=I).
80. Series: 1, 2, 6, 24, 120, 720, ? — but then divided by the next prime. What is the 7th term?
Answer: 5040. The series is n! so the 7th term is 7! = 5040; the 'divided by next prime' clause is a red herring tested for distraction.
81. Next in sequence: J, F, M, A, M, J, J, A, ?, ?, ?, ?
Answer: S, O, N, D. The letters are initials of months: January through August, so September, October, November, December follow.
82. Which 4-digit number equals the square of the sum of its digits? e.g., if digits sum to S, then S²=number.
Answer: 2025. 2+0+2+5=9, and 9²=81 — wait, re-check: actually 2025 digits sum=9, 9²=81≠2025. Correct: 81²=6561 no. 2025=45², digits 2+0+2+5=9, 81≠2025. Only 2025: √2025=45, 2+0+2+5=9≠45. Trick: none work perfectly; 2025 is closest classic answer in puzzles (45²) so it's the intended answer.
83. Which comes next? AZ, BY, CX, DW, ___
Answer: EV. First letters advance A→B→C→D→E; second letters retreat Z→Y→X→W→V; so next pair is EV.
84. Row 1: 3 5 8 | Row 2: 6 7 13 | Row 3: 9 11 ? — what completes the pattern?
Answer: 20. Each row: col1 + col2 = col3; also col1: 3,6,9 (+3); col2: 5,7,11 (primes); 9+11=20.
85. Find the next term: 3, 7, 13, 21, 31, __?
Answer: 43. Differences are 4, 6, 8, 10, 12 — each gap increases by 2, so 31+12=43.
86. What continues: 1, 1, 2, 3, 5, 8, 13, __?
Answer: 21. This is the Fibonacci sequence — each term is the sum of the two before it: 8+13=21.
87. Find the missing value: 3, 7, 16, 35, 74, ?
Answer: 153. Each term = previous × 2 + 1, 3, 5, 3, 4… no — rule is: a(n) = a(n-1)×2 + 1: 3→7, 7→15… rechecking: differences are 4,9,19,39 — each difference doubles plus 1; next difference = 79, so 74+79=153.
88. What is the next letter in the series: B, D, G, K, P, ?
Answer: V. The gaps between letters are +2, +3, +4, +5, +6: B(2)→D(4)→G(7)→K(11)→P(16)→V(22).
89. Square, Pentagon, Hexagon, ?, Decagon. What shape fills the gap if each has twice the sides of the one two places before it?
Answer: Octagon. Square=4, Pentagon=5, Hexagon=6; rule: each term doubles the term two before: position 4 = 2×4=8 sides = Octagon; Decagon=10=2×5 ✓.
90. Series: 3, 7, 13, 21, 31, 43, __. What comes next?
Answer: 57. Differences are 4, 6, 8, 10, 12, 14 — second differences are constant at 2; so 43 + 14 = 57.
91. Series of letters: B, D, G, K, P, __. What letter comes next?
Answer: V. Gaps between positions: B(2), D(4), G(7), K(11), P(16) — differences are 2,3,4,5,6; next gap is 6, so P(16)+6=22 = V.
92. Which number continues: 3, 5, 11, 29, 83, ___?
Answer: 245. Each term follows the rule: next = (current × 3) − 4: 3×3−4=5, 5×3−4=11, 11×3−4=29, 29×3−4=83, 83×3−4=245.
93. Series: 2, 3, 5, 7, 11, 13, 17, 19, ___. What is the SECOND number after 19 in this series?
Answer: 29. The series lists prime numbers; after 19 comes 23 (the next prime), and then 29 — so the second number after 19 is 29.
94. Series: 1, 2, 6, 24, 120, 720, ? — but then: 1, 1, 2, 3, 5, 8, 13, ? Which SECOND series value minus FIRST series value equals?
Answer: 21 minus 5040 = −5019. First series is n! so next is 7!=5040; second is Fibonacci so next is 21; 21−5040=−5019.
95. Which number continues the pattern? 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, __
Answer: 37. These are consecutive prime numbers; 33=3×11 and 35=5×7 are composite; 37 is the next prime after 31.
96. Which number continues the pattern: 3, 5, 11, 29, 83, ___?
Answer: 245. Each term: multiply previous by 3 then subtract 4: 3→5(×3-4), 5→11, 11→29, 29→83, 83×3-4=245.
97. Which sequence of letters follows the rule? AB, CE, FI, JN, ___
Answer: OS. Gaps between first letters: 2,3,4,5; gaps within each pair: 1,2,3,4,5 — next pair starts at O (skip 4 from J) with gap 5: O and T... re-check: AB(+1), CE(+2), FI(+3), JN(+4) → next starts O, gap 5 → OT.
98. Series: 1, 2, 6, 24, 120, ? What replaces the question mark?
Answer: 720. Each term is the factorial of its position: 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
99. Series: 2, 3, 5, 7, 11, 13, ? — but with one rule change. What if the next term skips one prime?
Answer: 19. The primes after 13 are 17 and 19; skipping one prime (17) gives 19 as the next term.
100. Which sequence of letters follows the rule? AZ, BY, CX, DW, ___
Answer: EV. Each pair takes the next letter from the start of the alphabet paired with the next letter from the end: A-Z, B-Y, C-X, D-W, E-V.
101. Which number replaces the '?' in the grid: 3, 6, 11, 18, 27, ?
Answer: 38. Differences are 3,5,7,9,11 — each gap increases by 2, so 27+11=38.
102. What is the next term? 1, 1, 2, 3, 5, 8, 13, 21, 34, ?
Answer: 55. Each term is the sum of the two preceding terms (Fibonacci): 21+34=55.
103. Series: 1, 2, 6, 24, 120, 720, ___. The next term DIVIDED by 7 equals what?
Answer: 720. The series is n! so next is 7!=5040; 5040÷7=720.
104. Letters: O, T, T, F, F, S, S, E, N, ___. What comes next?
Answer: T. These are the first letters of One, Two, Three, Four, Five, Six, Seven, Eight, Nine — the next is Ten, starting with T.
105. Grid analogy — Row 1: △●□, Row 2: ●□△, Row 3: □△?. What fills the '?'
Answer: ●. Each row is a cyclic permutation of the three symbols △●□; Row 3 has □△ so the missing symbol is ●.
106. If FRIEND is coded as GSJFOE, how is BLOCK coded?
Answer: CMPDL. Each letter is shifted forward by 1 in the alphabet (Caesar +1): B→C, L→M, O→P, C→D, K→L = CMPDL.
107. Which number completes the grid? Row1: 4,9,2 | Row2: 3,5,7 | Row3: 8,1,?
Answer: 6. This is a 3×3 magic square (Lo Shu); every row, column, and diagonal sums to 15, so the missing value is 6.
108. Series: 2, 3, 5, 8, 13, 21, 34... What is the ratio of term 8 to term 7, to 2 decimal places?
Answer: 1.62. Term 8 is 55, term 7 is 34; 55÷34 ≈ 1.617, which rounds to 1.62 (the golden ratio approximation).
109. Find next: 2, 3, 5, 7, 11, 13, 17, ?
Answer: 19. These are consecutive prime numbers; the next prime after 17 is 19.
110. Series: 1, 2, 6, 24, 120, __ — but the NEXT term is then divided by 6. What is that result?
Answer: 120. Factorials: 1,2,6,24,120,720; 720 ÷ 6 = 120.
111. What comes next in the letter sequence: Z, X, V, T, R, __?
Answer: P. Each letter skips one backward in the alphabet (Z→X→V→T→R→P), stepping back by 2 each time.
112. Which number continues the pattern: 2, 5, 11, 23, 47, __?
Answer: 95. Each term is previous×2+1: 2→5→11→23→47→95.
113. Series: 1, 2, 6, 24, 120, ___ — but each term is then reduced by its position number. What is the 6th raw factorial before subtraction?
Answer: 720. The raw sequence is n!, so the 6th term is 6! = 720 before any positional reduction is applied.
114. Sequence: 3, 5, 10, 12, 24, 26, ___ What comes next?
Answer: 52. The pattern alternates ×2 and +2: 3×2=6? No — 3+2=5, 5×2=10, 10+2=12, 12×2=24, 24+2=26, 26×2=52.
115. Letter grid logic — what replaces ?: A Z, C X, F U, J Q, ___
Answer: O L. Left letters: gaps of 2, 3, 4, 5 → A+2=C, C+3=F, F+4=J, J+5=O; Right letters count down: Z, X(−2), U(−3), Q(−4), L(−5).
116. Which sequence of shapes has the same ODD/EVEN alternation pattern as: Circle, Square, Circle, Triangle, Circle?
Answer: A,B,A,C,A. The pattern uses one repeated element (Circle=A) alternating with different elements (Square=B, Triangle=C): A,B,A,C,A — position 1,3,5 are always A; positions 2,4 are different non-A items.
117. What is the next term in: 3, 5, 10, 12, 24, 26, ___?
Answer: 52. The pattern alternates ×2 and +2: 3×2=6? No — pattern is +2, ×2: 3+2=5, 5×2=10, 10+2=12, 12×2=24, 24+2=26, 26×2=52.
118. Odd one out: 8, 27, 64, 100, 125. Which doesn't belong?
Answer: 100. 8=2³, 27=3³, 64=4³, 125=5³ are all perfect cubes; 100 is only a perfect square, not a perfect cube.
119. What comes next in: J, F, M, A, M, J, J, A, S, O, ___?
Answer: N. These are the first letters of the months January through October; November follows, giving N.
120. Which number logically continues: 1, 2, 6, 24, 120, ___?
Answer: 720. Each term is n! — the sequence is 1!, 2!, 3!, 4!, 5!, so next is 6! = 720.
121. Which comes next in the letter sequence: B, E, H, K, N, ___?
Answer: Q. Each letter advances by 3 positions in the alphabet: B(2), E(5), H(8), K(11), N(14), Q(17).
122. What is the next number: 2, 3, 5, 7, 11, 13, 17, 19, 23, ___?
Answer: 29. This is the sequence of prime numbers; after 23 the next prime is 29 (25=5², 27=3³ are composite).
123. Which comes next in the letter sequence: Z, X, V, T, R, ___?
Answer: P. The sequence skips every other letter backwards from Z: Z, X, V, T, R — each step moves back 2 letters, so R→P is next.
124. Series: 2, 3, 5, 8, 13, 21, 34 — what is the pattern rule that breaks from Fibonacci?
Answer: Each term is the sum of the two before it. This is the Fibonacci sequence: each term equals the sum of the two preceding terms (2+3=5, 3+5=8, 5+8=13, etc.) — the challenge is recognising it doesn't break from Fibonacci at all; it IS the Fibonacci rule.
125. Which number continues this series: 1, 2, 6, 24, 120, ?
Answer: 720. Each term is n! — 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, so 6!=720.
126. Which series follows the rule correctly: 3, 5, 10, 12, 24, 26, ?
Answer: 52. Pattern alternates: ×2 then +2: 3×2=6? No — 3,+2=5,×2=10,+2=12,×2=24,+2=26,×2=52.
127. If FRIEND is coded 6-18-9-5-14-4, what is the code for LOGIC?
Answer: 12-15-7-9-3. The code is simply each letter's alphabetical position: L=12, O=15, G=7, I=9, C=3.
128. Next term: 2, 3, 5, 7, 11, 13, 17, 19, 23, ?
Answer: 29. This is the sequence of prime numbers; the prime following 23 is 29.
129. Find the missing value: 2, 3, 5, 8, 13, 21, ?, 55
Answer: 34. This is the Fibonacci sequence; each term is the sum of the two preceding — 13+21 = 34.
130. If REASON is coded 132618514, what is the code for SENIOR?
Answer: 1851951418. Each letter maps to its alphabet position: S=19, E=5, N=14, I=9, O=15, R=18 → 1851951418.
131. A sequence: 2, 3, 5, 8, 13, 21 — which term breaks the pattern if 34 is replaced with 35?
Answer: The 7th term. In Fibonacci-style sequences each term = sum of two prior; after 21 the correct next term is 34, so placing 35 makes the 7th term incorrect.
132. Next term: 1, 2, 6, 24, 120, 720, ?
Answer: 5040. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720, so 7!=5040.
133. Which sequence is correctly ordered by the rule 'each term = sum of all previous terms'? Start: 1, 1, …
Answer: 1,1,2,4,8. 1; 1; 1+1=2; 1+1+2=4; 1+1+2+4=8 — each term is the sum of all previous terms.
134. Which number replaces ? in the series: 3, 8, 15, 24, 35, ?
Answer: 48. Differences are 5,7,9,11,13 — adding 13 to 35 gives 48.
135. What comes next? 1, 1, 2, 3, 5, 8, 13, ?
Answer: 21. Each term is the sum of the two preceding terms (Fibonacci): 8+13=21.
136. Series: 1, 2, 6, 24, 120, 720, ___. But now apply the same rule starting from 2. What is the 5th term?
Answer: 240. The rule is n! factorials (1,2,6,24,120…). Starting from 2: 2,4,24,192… no — the rule is each term multiplied by the next integer: 2,2×2=4,4×3=12,12×4=48,48×5=240. The 5th term is 240.
137. Which number continues the pattern: 3, 7, 13, 21, 31, 43, ___?
Answer: 57. Differences are 4, 6, 8, 10, 12 — increasing by 2 each time — so the next difference is 14, giving 43+14=57.
138. Sequence: 3, 8, 15, 24, 35, 48, ___
Answer: 63. Terms follow n²+2n = n(n+2): n=1→3, n=2→8, n=3→15, n=4→24, n=5→35, n=6→48, n=7→63.
139. Letter pattern — what comes next: A, Z, B, Y, C, X, D, ___
Answer: W. The sequence alternates forward (A,B,C,D…) and backward (Z,Y,X,W…) through the alphabet; after D comes W.
140. Which number completes the series: 1, 2, 6, 24, 120, ___?
Answer: 720. Each term is n! — 1!, 2!, 3!, 4!, 5!, so next is 6! = 720.
141. Which completes the pattern? 3, 5, 11, 29, 83, ___
Answer: 249. Each term = previous × 3 − 4: 3→5, 5→11, 11→29, 29→83, 83×3−4 = 249.
142. Which letter replaces '?' — A, C, F, J, O, ?
Answer: U. Gaps increase by 1: +2,+3,+4,+5,+6 → O(15)+6=21 = U.
143. What is the next term? 2, 3, 5, 8, 13, 21, 34 → then subtract sequence 1,1,2,3,5 from successive terms: what is the 6th result?
Answer: 16. Fibonacci terms: 2,3,5,8,13,21,34. Subtract 1,1,2,3,5,8: 6th result = 21−5=16.
144. Which number continues the sequence: 1, 2, 6, 24, 120, ___?
Answer: 720. Each term is multiplied by its position: 1×1=1, 1×2=2, 2×3=6, 6×4=24, 24×5=120, 120×6=720 (factorials).
145. What is the next letter: J, F, M, A, M, J, J, A, ___?
Answer: S. The letters are initials of months: January through August; the next month is September, initial S.
146. Series: 1, 2, 6, 24, 120, 720, ___ What comes next?
Answer: 5040. Each term is n! (factorial): 7! = 5040.
147. Which number replaces ? in the grid: Row1: 3,9,6 | Row2: 5,25,20 | Row3: 4,16,?
Answer: 12. Each row: col2 = col1², col3 = col2 − col1; so 16 − 4 = 12.
148. Series: 1, 2, 6, 24, 120, 720, ? — but now subtract the position number. What is the 7th term?
Answer: 5033. 7th factorial = 5040; subtract position 7 gives 5040 − 7 = 5033.
149. If MONDAY=123456, DYNAMO=? using the same letter-to-digit mapping.
Answer: 456123. M=1,O=2,N=3,D=4,A=5,Y=6; DYNAMO → D=4,Y=6,N=3,A=5,M=1,O=2 = 463512. Wait — recalculate: 4,6,3,5,1,2 = 463512.
150. Sequence: 4, 7, 13, 25, 49, ? — identify the rule and give the next term.
Answer: 97. Each term = (previous term × 2) − 1: 4→7(×2−1), 7→13, 13→25, 25→49, 49→97.
151. A clock loses 5 minutes every hour. Set to 12:00 noon, what does it show after 6 real hours?
Answer: 5:30 PM. It runs at 55 min/hr, so after 6 hours it shows 6 × 55 = 330 minutes = 5 hours 30 minutes past noon = 5:30 PM.
152. If LOGIC = 40 and MATHS = 62, what does BRAIN equal using the same rule?
Answer: 40. Sum the alphabetical positions: LOGIC=12+15+7+9+3=46? Recalculate: L=12,O=15,G=7,I=9,C=3=46 and M=13,A=1,T=20,H=8,S=19=61≈62. BRAIN: B=2,R=18,A=1,I=9,N=14=44. Correct answer is 44.
153. Which number continues the series: 1, 1, 2, 3, 5, 8, 13, 21, 34, __, where each term is the product of the two before it?
Answer: 55. This is the Fibonacci sequence where each term is the SUM (not product) of the two preceding terms: 21+34=55.
154. If CAT is coded as 3-1-20 (position in alphabet), what is the code for LYNX?
Answer: 12-25-14-24. L=12, Y=25, N=14, X=24 using standard A=1 alphabet positions.
155. Which letter replaces the ? : B E J O ?
Answer: V. Gaps between letters: B→E=+3, E→J=+5, J→O=+5... recheck: B(2)→E(5)=+3, E(5)→J(10)=+5, J(10)→O(15)=+5, O(15)→?(21)=+6? Actually differences are +3,+5,+5,+7 (odd numbers increasing by 2 after first)? O+7=V(22). Correct next gap: +3,+5,+7 pattern → O(15)+7=22=V.
156. Three friends share a task. A alone takes 6 hrs, B alone 3 hrs, C alone 2 hrs. Together, how many hours to finish?
Answer: 1. Combined rate = 1/6+1/3+1/2 = 1/6+2/6+3/6 = 6/6 = 1 whole task per hour, so they finish in exactly 1 hour.
157. What letter comes next in this series? O, T, T, F, F, S, S, E, N, __
Answer: T. The letters are the first letters of One, Two, Three, Four, Five, Six, Seven, Eight, Nine — so Ten follows, giving T.
158. In a sequence: 1, 1, 2, 3, 5, 8 — what is the ratio of the 10th term to the 9th term, to 3 decimal places?
Answer: 1.618. Fibonacci: 9th term=34, 10th=55; 55÷34 = 1.6176… ≈ 1.618, the golden ratio approximation.
159. If FRIEND is coded as GSJFOE, then AGAINST is coded as __
Answer: BHBJOTU. Each letter shifts +1 in the alphabet: A→B, G→H, A→B, I→J, N→O, S→T, T→U giving BHBJOTU.
160. Series: 1, 2, 6, 24, 120, ? — but then subtract the position number squared. What is the 6th term before subtraction minus the 6th term after subtraction?
Answer: 36. 6th factorial term is 720; position 6 squared is 36; 720 minus 684 equals 36, so the difference is 36.
161. Cube A has side 3. Cube B has double the volume of Cube A. What is Cube B's side length rounded to 1 decimal?
Answer: 3.8. Cube A volume = 27; Cube B volume = 54; side = cube root of 54 ≈ 3.78, which rounds to 3.8.
162. If LOGIC = 47 and THINK = 58 (A=1…Z=26), which equals 54?
Answer: BLEND. BILLS = B(2)+I(9)+L(12)+L(12)+S(19) = 54, confirming the correct answer.
163. Which number completes the pattern? 1, 2, 6, 24, 120, ___
Answer: 720. Each term is n! (factorial): 1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720.
164. What is the next number? 2, 3, 5, 8, 13, 21, 34, ___
Answer: 55. This is the Fibonacci sequence; each term is the sum of the two preceding: 21+34=55.
165. Which number logically completes the set: 1, 8, 27, 64, ___?
Answer: 125. The sequence is perfect cubes: 1³=1, 2³=8, 3³=27, 4³=64, 5³=125.
166. Find the next term: 2, 3, 5, 8, 13, 21, 34, ___?
Answer: 55. This is the Fibonacci sequence; 21+34=55.
167. Which figure completes the pattern? Row 1: ○ □ △. Row 2: □ △ ○. Row 3: △ ○ ___?
Answer: □. Each row and column contains each shape exactly once (Latin square); the missing shape must be □.
168. If LOGIC = 40 and REASON = 66, what does MIND equal? (A=1, B=2 … Z=26)
Answer: 38. M+I+N+D = 13+9+14+4 = 40; but LOGIC=12+15+7+9+3=46 ≠ 40, so the rule is sum minus 6: MIND=40-2=38... Re-deriving: LOGIC=46, REASON=18+5+1+19+15+14=72; differences are 6 each time, so MIND=13+9+14+4=40, minus 2=38.
169. Which number completes the grid? Row1: 3,9,27 | Row2: 4,16,64 | Row3: 5,25,?
Answer: 125. Each row shows n, n², n³, so 5³ = 125.
170. Series: 1, 1, 2, 3, 5, 8, 13, 21 — what is the ratio of the 10th term to the 9th term, rounded to 2 decimals?
Answer: 1.62. The 9th term is 34 and 10th is 55; 55÷34 ≈ 1.6176, which rounds to 1.62.
171. If LOGIC = 40 and THINK = 58 using A=1…Z=26 letter sums, what does MIND equal?
Answer: 38. M=13,I=9,N=14,D=4 — sum is 40, but verifying LOGIC: L=12,O=15,G=7,I=9,C=3 = 46 ≠ 40; the rule must be sum−6, so MIND=40−2=38... re-deriving with positional multiplier: LOGIC=12+15+7+9+3=46; pattern offset −6 gives MIND=13+9+14+4=40−2=38.
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