# PE 3 - Puzzles | LR - Puzzles

**Answer the next 4 questions based on the information given below.**

A restaurant in Bhopal has four tables. Tables 1 and 3 have two seats each while tables 2 and 4 have four seats each. Customer(s), whether single or in groups, are directed towards relevant tables to optimize seating capacity. Any set of at most two customers is first directed towards table 1 or 3. A lower numbered table is preferred over a higher numbered table. Hence, table 1 is preferred over table 3. If neither table is available, they are directed to the higher capacity tables (with table 2 being preferred before table 4, in case both of these are available). Any group of more than two customers directly goes to tables 2 or 4, with table 2 being preferred first.

No customer is made to wait if any of the tables is free.

A table is said to be “available” only if there is no one sitting on it. Two different groups (individual person or group) cannot simultaneously occupy the same table.

The outlet opened at 8:15 a.m. on a certain day. The table below shows the list of all customers entering the outlet till 9:30 am.

A group of at most 2 people spends exactly 30 minutes or 35 minutes in the outlet while a group of more than 2 people spends exactly 50 minutes or 55 minutes, depending on their table number. Customers on tables 1 and 3 spend 30 minutes or 50 minutes (depending on ≤ 2 or > 2 people respectively) while customers on tables 2 and 4 spend 35 minutes or 55 minutes (depending on ≤ 2 or > 2 people respectively).

If a customer/group does not get a table within 10 minutes of their entry time, they return back.

**PE 3 - Puzzles | LR - Puzzles**

Which of these customers had to return back from the outlet?

- (a)
Karan, Deepak and Sachin

- (b)
Bhanu, Nikhar and Roomesh

- (c)
Hardik and Arpit

- (d)
Vishal and Rahul

Answer: Option B

**Explanation** :

First list the table allocation priority for every kind of group:

**1 person or 2 people **

Table 1 (30 minutes) > Table 3 (30 minutes) > Table 2 (35 minutes) > Table 4 (35 minutes)

**More than 2 people**

Table 2 (55 minutes) > Table 4 (55 minutes)

Also, two different groups cannot simultaneously occupy the same table. Hence, based on the entering time of the people, the entry and exit time of each person can be plotted as shown below:

**Harsh and Prasukh enter 1st and occupy Table 1**:

**Gautam, Vimal and Rohit enter next and occupy Table 2**:

**Akshay enters next and occupies Table 3**:

**Vikash and Pankaj enter next and occupy Table 1**:

**Karan, Deepak and Sachin enter next and occupy Table 4:**

**Hardik and Arpit enter next and occupy Table 3**:

**Vishal and Rahul enter next and occupy Table 2**:

Hence, the group of Bhanu, Nikhar and Roomesh had to return back as their waiting time was 11 minutes.

Hence, option (b).

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

What was the waiting time (in minutes) for Vishal and Rahul before they got a table at the restaurant?

- (a)
5

- (b)
4

- (c)
3

- (d)
2

Answer: Option D

**Explanation** :

Consider the solution to the first question.

The waiting time for Vishal and Rahul was 2 minutes (9:13 a.m. to 9:15 a.m.) before they got a table.

Hence option (d).

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

If these were the only guests who came that day, which of the four tables was occupied for the least amount of time (in minutes)?

- (a)
1

- (b)
2

- (c)
3

- (d)
4

Answer: Option D

**Explanation** :

Consider the solution to the first question.

The occupancy time for each table was:

Table 1: 30 + 30 = 60 minutes

Table 2: 55 + 35 = 90 minutes

Table 3: 30 + 30 = 60 minutes

Table 4: 55 minutes

Hence, table 4 was occupied for the least amount of time.

Hence option (d).

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

Which of these pairs of tables had the same total number of people sitting on it during the given period?

- (a)
1 and 3

- (b)
2 and 4

- (c)
1 and 4

- (d)
None of these

Answer: Option D

**Explanation** :

Consider the solution to the first question.

The total number of people on each table is:

Table 1: 4 (Harsh, Prasukh, Vikas and Pankaj) = 4

Table 4: 4 (Gautam, Vimal, Rohit, Vishal and Rahul) = 5

Table 2: 3 (Akshay, Hardik and Arpit) = 3

Table 4: 3 (Karan, Deepak and Sachin) = 3

Hence, option (d).

Workspace:

**Answer the next 4 questions based on the information given below:**

Eight people - P, Q, R, S, T, U, V and W are sitting around a table and playing a game.

- P starts the game by putting a 2-digit number of coins in the middle of the table.
- Now, Q may or may not remove some coins such that the number of coins remaining on the table is a two-digit perfect square.
- Next, R may or may not add some coins such that the number of coins remaining on the table is again a two-digit perfect square.
- Subsequently S, T, U, V and W may or may not remove / add coins alternately in that order such that the number of coins on the table is always a 2-digit perfect square.
- One round is said to be completed when all 8 people have completed their turn.

- Number of coins added / removed is always a whole number.
- Coins once removed cannot be used again.

**PE 3 - Puzzles | LR - Puzzles**

What is the smallest number of distinct marbles required to complete one round?

Answer: 16

**Explanation** :

Each person adds / removes whole number of coins.

For total coins used to be minimum, each person should not add / remove any coins i.e., 0 coins.

This is possible when P puts number of coins which is a perfect square. Least 2-digit perfect square = 16.

Subsequently, if Q, R, S, T, U, V and W do not remove / add coins then also the conditions of the game are met.

Hence, the least number of coins required to complete one round is 16.

Hence, 16.

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

What is the maximum number of coins required to complete one round?

Answer: 294

**Explanation** :

Maximum number of coins required wil be when the each person removing coins leaves the smallest number of 2-digit perfect square and every person adding leaves highest number of 2-digit perfect square.

P should also start with the highest possible 2-digit number.

∴ P puts 99 coins on the table.

Q removes 83 coins and leaves 16 coins on the table.

R now adds 65 coins to make total coins as 81

S, T, U, V and W will similaly continue the process.

∴ Total coins added = 99 (P) + 65 (R) + 65 (T) + 65 (V) = 294

Hence, 294.

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

What cannot be the number of coins removed by S?

- (a)
9

- (b)
65

- (c)
48

- (d)
14

Answer: Option D

**Explanation** :

Number of coins removed by S will be difference between 2 2-digit perfect squares.

Option (a): 9 = 25 - 16

Option (b): 65 = 81 - 16

Option (c): 48 = 64 - 16

Option (d): 14 cannot be the difference between 2 2-digit perfect squares.

Hence, option (d).

Workspace:

**PE 3 - Puzzles | LR - Puzzles**

Which of the following can be the sum of the total coins added by R and T.

- (a)
51

- (b)
123

- (c)
52

- (d)
None of these

Answer: Option C

**Explanation** :

Difference between any 2 2-digit perfect squares can be as follows:

Total coins added by R and T can be 24 + 28 = 52.

Hence, option (c).

Workspace:

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