"Four friends each have a different job and a favorite color. Ana isn't the doctor. The teacher loves blue. Ben's favorite is red..." — and from a handful of such clues, you're expected to work out exactly who does what. It sounds overwhelming, but there's a tool that makes these puzzles almost mechanical: a grid. Fill it with checks and X's as the clues come, and the solution reveals itself. This chapter teaches the grid method plus the special arithmetic for calendar and clock puzzles, turning intimidating brain-teasers into orderly, solvable tasks.
Puzzle questions come in a few distinct sub-types. Grid (logic) puzzles match people to attributes (jobs, colors, ages) from clues. Calendar puzzles ask what day of the week a date falls on. Clock puzzles involve the angles and positions of clock hands. Each sub-type has its own winning method.
On the Civil Service Exam, puzzles appear in Analytical Reasoning, often as a set sharing one scenario. They test systematic deduction (grids) and specialized arithmetic (calendars, clocks). A clear method for each makes them dependable.
The difficulty ranges from intermediate to advanced. The keys are: for grids, build a table and process clues from most to least restrictive; for calendars, count days modulo 7 and account for leap years; for clocks, use the hands' constant speeds. This lesson builds all three.
After completing this lesson you will be able to:
You should be comfortable with:
A quick refresher on the two special tools. For calendars: the week repeats every 7 days, so "how many days later" questions come down to the remainder when divided by 7 (14 days later = same weekday; 16 days later = 2 weekdays later). For clocks: the minute hand moves 6° per minute (360° ÷ 60) and the hour hand moves 0.5° per minute (30° per hour ÷ 60). Keep these two facts ready — they power every calendar and clock puzzle.
Structured deduction and time arithmetic are practical skills:
The exam tests puzzles because systematic, multi-constraint reasoning is a core analytical ability.
We'll cover grids, then calendars, then clocks.
When a puzzle matches people to attributes (e.g., 4 people, 4 jobs, 4 colors), draw a grid with people as rows and attributes as columns. Mark a confirmed match with a check (✓) and an impossible match with an X as you process clues.
Analogy: A logic grid is like a Sudoku for words. Each ✓ and X you place constrains the rest, and the constraints cascade until only one arrangement survives. You're not guessing — you're eliminating.
Handle clues from most to least restrictive:
Starting with direct facts gives you anchors; conditional clues make sense only after the grid is partly filled.
Once a match is confirmed (✓), every other cell in that same row and column becomes impossible (X) — each person has one job, each job one person. This cascade often forces new matches you weren't told directly: if a column has X's in all cells but one, that last cell must be a ✓.
To find a day of the week, convert the gap to a number of days and reduce modulo 7:
If January 1 is a Monday, what day is January 15? 15 − 1 = 14 days later. 14 ÷ 7 = 2 remainder 0 → same weekday → Monday.
For a non-multiple: 16 days later has remainder 2, so 2 weekdays after Monday = Wednesday.
Year-spanning shifts: a common (non-leap) year shifts a given calendar date forward by 1 weekday; a leap year (containing Feb 29) shifts it by 2 weekdays, because it has one extra day. So the same date next year is usually one weekday later — two if February 29 falls in between.
Leap-year rule: a year is a leap year if divisible by 4, except century years, which must be divisible by 400 (2000 was a leap year; 1900 was not).
The minute hand moves 6° per minute; the hour hand moves 0.5° per minute. The minute hand gains on the hour hand at 6 − 0.5 = 5.5° per minute. To find when the hands overlap or are a certain angle apart, set up the angle as a function of time and solve.
How many minutes after 3:00 do the hands first overlap? At 3:00, the hour hand is at 90° (3 × 30°), the minute hand at 0° — a 90° gap. The minute hand closes it at 5.5°/min: 90 ÷ 5.5 ≈ 16.36 minutes (about 3:16 and a bit).
The angle between the hands at H:MM is |30 × H − 5.5 × MM| degrees (taking the smaller angle if over 180°).
For grids especially, once the arrangement looks complete, re-check every original clue. A single overlooked clue can yield an internally consistent but wrong solution. The final pass is essential.
With the methods built, let's picture, tabulate, and drill.
Puzzles use methods plus a few formulas:
| Tool | Rule |
|---|---|
| Grid | ✓ confirmed, X impossible; cascade row/column |
| Clue order | direct facts → eliminations → conditionals |
| Calendar (gap) | days later mod 7 |
| Common year shift | +1 weekday |
| Leap year shift | +2 weekdays |
| Leap year test | ÷4, except centuries need ÷400 |
| Minute hand | 6° per minute |
| Hour hand | 0.5° per minute |
| Hands' relative speed | 5.5° per minute |
| Angle at H:MM |
| When the puzzle… | Do this… |
|---|---|
| matches people to attributes | build a grid |
| gives a direct "X is the Y" | mark ✓ first |
| gives "X is not Y" | mark X |
| gives "if… then…" | apply last, after anchoring |
| asks a day of the week | count days mod 7; mind leap years |
| spans years | +1 (common) or +2 (leap) weekday per year |
| involves clock hands | use 6°/min and 0.5°/min |
Step 1 — Identify the sub-type: grid, calendar, or clock. ↓ Step 2 (grid) — Build the grid and mark direct facts (✓), then eliminations (X), then conditionals. ↓ Step 2 (calendar) — Count the day gap and reduce mod 7, accounting for leap years. ↓ Step 2 (clock) — Use the hand speeds (6°/min, 0.5°/min) to set up the angle and solve. ↓ Step 3 — Cascade/compute, then verify against every clue (grids) or double-check the arithmetic (calendars/clocks).
Why the clue order matters most (grids): starting with direct facts creates anchors that make eliminations cascade. Beginning with vague conditional clues, before any anchor exists, stalls the whole puzzle.
Example 1 (calendar). If March 1 is a Wednesday, what day is March 8? Solution: 7 days later → same weekday → Wednesday. Difficulty: ★☆☆☆☆
Example 2 (grid, direct). Three people (A, B, C) have three jobs (nurse, clerk, guard). A is the nurse. B is not the clerk. Who is the guard? Thinking: A = nurse. B not clerk → B = guard. C = clerk. Solution: B is the guard. Difficulty: ★★☆☆☆
Example 3 (calendar gap). If January 1 is a Sunday, what day is January 20? Thinking: 19 days later; 19 ÷ 7 = 2 remainder 5 → 5 weekdays after Sunday. Solution: Sun → Fri (Mon, Tue, Wed, Thu, Fri) = Friday. Difficulty: ★★★☆☆
Example 4 (clock angle). What is the angle between the hands at 3:00? Solution: |30 × 3 − 5.5 × 0| = 90°. Difficulty: ★★☆☆☆
Example 5 (grid cascade). Four people (P, Q, R, S) have four colors (red, blue, green, yellow). P likes red. Q likes blue. R does not like green. Who likes yellow and who likes green? Thinking: P = red, Q = blue. R and S have green/yellow. R not green → R = yellow, S = green. Solution: R = yellow, S = green. Difficulty: ★★★☆☆
Example 6 (clock overlap). After how many minutes past 3:00 do the hands overlap? Solution: Gap 90° closing at 5.5°/min → 90 ÷ 5.5 ≈ 16.36 minutes. Difficulty: ★★★★☆
Example 7 (year shift). If May 5, 2023 is a Friday, what day is May 5, 2024? (2024 is a leap year, and Feb 29, 2024 falls between the two dates.) Thinking: A leap year with Feb 29 in the interval shifts the date +2 weekdays. Solution: Fri + 2 = Sunday. Difficulty: ★★★★☆
Example 8 (grid conditional). Three friends (X, Y, Z) play three sports (chess, tennis, golf). X does not play chess. If Y plays tennis, then Z plays golf. Y plays tennis. Who plays what? Thinking: Y = tennis → (by the conditional) Z = golf → X = chess. But X doesn't play chess — contradiction. So re-examine: since Y = tennis and Z = golf forced, X = chess, which violates "X not chess." Therefore the given clues are inconsistent unless Y ≠ tennis — but we're told Y plays tennis, so this illustrates checking consistency. Corrected setup: if instead "X does not play golf," then Y = tennis → Z = golf → X = chess (consistent). Solution: With the consistent version (X not golf): X = chess, Y = tennis, Z = golf. Lesson: verify conditional chains don't contradict a direct fact. Difficulty: ★★★★★
Example 9 (calendar, longer). If today is Monday, what day will it be after 100 days? Thinking: 100 ÷ 7 = 14 remainder 2 → 2 weekdays after Monday. Solution: Wednesday. Difficulty: ★★★★☆
Example 10 (clock angle at 4:20). Find the angle between the hands at 4:20. Thinking: |30 × 4 − 5.5 × 20| = |120 − 110| = 10°. Solution: 10°. Difficulty: ★★★★☆
Example 11 (grid full solve). Ana, Ben, Cita have pets: cat, dog, fish. Ana doesn't have the dog. Ben has the fish. Who has the cat? Thinking: Ben = fish. Ana not dog → Ana = cat. Cita = dog. Solution: Ana has the cat. Difficulty: ★★★☆☆
Example 12 (leap-year test). Is the year 1900 a leap year? Thinking: Divisible by 4 (475), but it's a century year, so it must be divisible by 400. 1900 ÷ 400 is not whole. Solution: No — 1900 is not a leap year (1900 ÷ 400 ≠ whole). (2000 is, since 2000 ÷ 400 = 5.) Difficulty: ★★★★☆
Puzzle questions split into sub-types, each with its own method. Grid (logic) puzzles: build a table, mark ✓ for confirmed and X for impossible, process clues from direct facts → eliminations → conditionals, and cascade X's across rows and columns until matches are forced — then verify against every clue. Calendar puzzles: count the day gap modulo 7, and remember a common year shifts weekdays by 1, a leap year by 2 (leap = divisible by 4, centuries by 400). Clock puzzles: use the minute hand (6°/min) and hour hand (0.5°/min), with the minute hand gaining 5.5°/min; the angle at H:MM is |30H − 5.5·MM|. Identify the sub-type, apply its tool, and verify — and even intimidating puzzles become orderly points.
| Sub-type | Key method |
|---|---|
| Grid | ✓/X table; direct → eliminate → conditional; cascade |
| Calendar gap | days mod 7 |
| Year shift | +1 common, +2 leap (Feb 29 in range) |
| Leap test | ÷4, centuries ÷400 |
| Minute hand | 6°/min |
| Hour hand | 0.5°/min |
| Hands gain | 5.5°/min |
| Angle at H:MM |
What's the best method for logic (grid) puzzles? Draw a grid of people versus attributes, mark confirmed matches with ✓ and impossible ones with X, and process clues from direct facts to conditionals. Each ✓ eliminates its row and column, cascading to force more matches.
How do I find a day of the week? Count the number of days between the dates and take the remainder when divided by 7 — that's how many weekdays to move forward. Account for leap years if February 29 falls in the span.
How does a leap year affect the weekday? A leap year has 366 days, so a given date shifts forward by 2 weekdays across it (versus 1 for a common year). Check the leap-year rule: divisible by 4, but century years must be divisible by 400.
How fast do clock hands move? The minute hand moves 6° per minute; the hour hand moves 0.5° per minute. The minute hand gains on the hour hand at 5.5° per minute, which is how you find overlaps and angles.
Why verify the grid at the end? Because a single overlooked clue can produce an arrangement that's internally consistent but wrong. A final pass through every clue catches such errors.
Tick them all and puzzle questions become orderly, dependable points — and you'll handle real scheduling, matching, and time problems with a systematic eye.
Put it to the test with 1,776 practice questions on this topic.