Puzzles for LIC AAO

A puzzle set usually carries four or five questions on one arrangement. Solve the arrangement once and every question takes seconds. Get one clue wrong and every question goes with it. That is why puzzles reward method more than any other reasoning topic. In the LIC AAO mains, where Reasoning questions carry three marks each, a five-question puzzle is worth 15 marks.

The method

1. Draw the grid. Number the positions. In box and floor puzzles, position 1 is the bottom unless the question says otherwise. For days, list them in order.
2. Place definite clues first. "B is at the bottom" or "P attends on Wednesday" fixes a position outright.
3. Place linked clues as cases. "C is three positions below D" gives two or three possibilities. Write each as a separate column.
4. Eliminate. Test every case against the remaining clues. Cross out a case the moment it breaks one. Only one case should survive.

Two habits make this faster. First, read all the clues once before you draw anything, and pick the most definite one as your starting point, even if it is clue 6. Second, use negative clues ("F does not hold ULIP") last. They rarely place anything alone but usually settle the final choice.

Worked puzzle 1: a box stack

Six boxes, A, B, C, D, E and F, are placed one above another. Position 1 is the bottom and position 6 the top.

1. Box B is at the bottom.
2. Box C is placed exactly three positions below box D.
3. Box A is placed immediately below box D.
4. Only one box is placed between box E and box A.
5. Box F is placed above box C.

Solving:

• Clue 1 is definite: B at 1.
• Clue 2 gives the pairs (C, D) = (1, 4), (2, 5) or (3, 6). Position 1 is B, so two cases remain.
• Case 1: C at 2, D at 5. Clue 3 puts A at 4. Clue 4 needs E two positions from A: 2 or 6. Position 2 is C, so E is at 6. F takes the only free position, 3, which is above C. Every clue holds.
• Case 2: C at 3, D at 6. Clue 3 puts A at 5. E would be at 3 or 7. Position 3 is C and 7 does not exist. This case fails.

Q1. Which box is at the top? E.

Q2. How many boxes are between B and A? Two, C and F.

Q3. Which box is immediately above F? A.

Worked puzzle 2: a floor puzzle with two variables

Seven people, A, B, C, D, E, F and G, live on seven floors of a building, one on each floor. Floor 1 is the lowest. Each holds a different insurance plan: Term, Endowment, ULIP, Pension, Health, Money-back and Child.

1. Only four people live below A.
2. The Term plan holder lives immediately above A.
3. Exactly two people live between A and E.
4. E holds the Endowment plan.
5. The Child plan holder lives immediately below E.
6. C lives on the lowest floor.
7. B lives immediately below F.
8. D lives on a floor above G.
9. The Health plan holder lives on the top floor.
10. B holds the Money-back plan.
11. F does not hold the ULIP plan.

Solving:

• Clue 1: four people below A puts A on floor 5.
• Clue 2: Term on floor 6.
• Clue 3: two people between A and E means their floors differ by three. Floor 8 does not exist, so E is on floor 2, holding Endowment (clue 4).
• Clue 5: Child on floor 1. Clue 6: C is on floor 1, so C holds Child.
• Clue 9: Health on floor 7.
• Free floors are 3, 4, 6 and 7. Clue 7 needs B and F on consecutive floors, B lower: (3, 4) or (6, 7). If B were on 6, B would hold Term, but clue 10 says B holds Money-back. So B on 3 with Money-back, F on 4.
• D and G take floors 6 and 7. Clue 8: D on 7 (Health), G on 6 (Term).
• ULIP and Pension remain for A and F. Clue 11: F holds Pension, A holds ULIP.

Q4. Who holds the Pension plan? F.

Q5. How many people live between C and G? Four: E, B, F and A.

Q6. Who lives immediately above the Money-back holder? F.

Wording that decides the answer

Practice puzzle

Six trainees, P, Q, R, S, T and U, each attend a training session on a different day from Monday to Saturday. Each attends a different module: Claims, Accounts, Underwriting, Legal, Marketing and Actuarial.

1. P attends on Wednesday.
2. Exactly two sessions are held between P's session and S's session.
3. The Marketing session is held on the day immediately before S's session.
4. Q attends the Marketing session.
5. T attends on the day immediately after R.
6. R attends the Claims session.
7. P attends the Underwriting session.
8. The Accounts session is held on a day before the Underwriting session.
9. S does not attend the Legal session.

Questions

1. Who attends on Thursday?
2. Which module is held on Saturday?
3. How many trainees attend between R and Q?
4. Who attends the Legal session?
5. On which day is the Accounts session held?
6. Who attends immediately after P?
7. How many sessions are held after the Underwriting session?

Solution

P is on Wednesday. Two sessions between P and S puts S on Saturday, because three days before Wednesday falls outside the week. Marketing is on Friday, and Q attends it. R and T need two consecutive free days from Monday, Tuesday and Thursday, so R is on Monday and T on Tuesday, leaving Thursday for U. R holds Claims. Accounts comes before Wednesday; Monday is Claims, so Accounts is Tuesday (T). U and S share Legal and Actuarial; S is not Legal, so S has Actuarial and U has Legal.

Answers

1. U.
2. Actuarial, taken by S.
3. Three: T, P and U.
4. U.
5. Tuesday.
6. U, on Thursday.
7. Three: Thursday, Friday and Saturday.

What to do next

• Solve one box, one floor and one scheduling puzzle every day this week. Note which clue you started from.
• Move on to seating arrangements, which use the same case method with left and right added.
• Once six-person puzzles take under five minutes, try the two- and three-variable sets in mains-level reasoning.