PROBLEM COLLECTION

You are facing north and A rectangular tank is filled with water. Each side The West and East phases of the tank are painted to look like an island. A small toy boat floats in the tank. On the boat is a small figurine which is facing north. You lift the right side of the tank. From the point of view of the figurine Which island appears to rise. The West side, East Side or Both or None.

Answer: East side

b_ab_a_a_ba_ Fill with correct alphabets. Such that it forms a repeating pattern. Pick from the options which is correct.

(a) bbaab (b) aabaa (c) bbabb (d) babab

Answer: (b) aabaa

I have plotted points on a coordinate plane and connected them in a specific order to form letters. These letters together spell out a word. Below, I will provide the coordinates of the points and indicate which points are connected using a specific symbol. The points belonging to each letter will be enclosed within curly brackets {} to indicate they form a single letter. Your task is to identify each letter and determine the complete word.

Notation:
Points are given as ordered pairs: (x, y).
Connections between points are denoted by → (e.g., (2,3) → (4,3) means these two points are connected by a line segment).
Each letter's points are enclosed in curly brackets {(x1,y1), (x2,y2), ...}.
A comma (,) within a letter's set indicates a new, separate line segment within that letter.

Here are the points and how they are connected:
{(0,1)→(0,2)→(1,3)→(2,2)→(2,1), (0,2)→(2,2)},
{(3,1)→(3,3)→(4,3)->(4,2)->(3,2), (3,2)→(4,1)},
{(5,3)→(7,3), (6,1)→(6,3)},
{(8,1)→(8,3)},
{(9,1)→(9,3)→(10,3), (9,2)→(10,2)},
{(11,1)→(11,3)},
{(13,1)→(12,1)→(12,3)→(13,3)},
{(14,1)→(14,3)},
{(15,1)→(15,2)→(16,3)→(17,2)→(17,1), (15,2)→(17,2)},
{(19,1)→(18,1)->(18,3)}

Solve and tell me what is the word.

Answer: ARTIFICIAL

The tuples represents 3×3 grids. Each tuple is ordered as: (a₁₁, a₁₂, a₁₃, a₂₁, a₂₂, a₂₃, a₃₁, a₃₂, a₃₃), where aᵢⱼ is the value in the i-th row and j-th column.

Given:
(1,0,1,0,0,0,1,0,1) ; (0,0,0,0,1,0,0,0,0) = (0,1,0,1,0,1,0,1,0)
(0,0,1,0,1,0,1,0,0) ; (0,0,0,0,0,1,0,1,1) = (1,1,0,1,0,0,0,0,0)

Task: Using the same rules, compute:
(1,1,0,1,0,1,0,1,1) ; (0,0,1,0,0,0,1,0,0)

Provide the answer as a tuple in grid order.

Answer: (0,0,0,0,1,0,0,0,0)

Eight friends P,Q,R,S,T,V,W and Y are sitting around a square table in such a way that four of them sit at four corners of the square table while four of them sit in the middle of each of the four sides. The ones who sit at the four corners face the centre while those who sit in the middle of the sides face outside.

S sits third to the right of P. P faces the centre. Y is not an immediate neighbor of P or S. T sits third to the right of R, who does not sit in the middle of any of the sides and also R is not an immediate neighbor of Y. Only one person sits between P and V. Q is not an immediate neighbor of V.

Now. If all the persons are made to sit in the alphabetic order in clockwise direction starting from P, the positions of how many (excluding P) will remain unchanged as compared to their original seating positions?

Answer: Q (other than P)

Eight friends – A, B, C, D, E, F, G, and H – are to be seated around a square table. The seats are numbered 1 to 8 in a clockwise direction, starting with seat 1 at the top left corner of the table. Those in seats 1, 3, 5, and 7 (the corner seats) face the center of the table. Those in seats 2, 4, 6, and 8 (the mid-side seats) face outwards.

The seating arrangement must also satisfy the following conditions:

1. G sits at seat 1.
2. Both of D's immediate neighbors face away from the center.
3. Both of B's immediate neighbors face the center.
4. F sits to the immediate right hand side of D.
5. H sits third to the left of E.
6. B sits second to the right of F.
7. A and F sit opposite each other.
8. D does not sit in the bottom seats.

Two seating arrangements are considered distinct only if at least one person has a different person sitting immediately to their left or right.

Based on this, how many distinct seating arrangements are possible? For each possible number of seating arrangements, list the position of each friend in the arrangement, starting from seat 1 and proceeding clockwise to seat 8.

a) 1 b) 2 c) 3 d) 4 e) 5

Answer: (b) 2
Arrangement 1: GFDBHACE
Arrangement 2: GFDBEACH

Sixty-four players seeded from seed 1 to seed 64 participated in a knock-out tennis tournament. Seed 1 is the highest seed and seed 64 is the lowest seed. The tournament would be played in six rounds i.e., first round, second round, third round, quarterfinals, semi finals and final. In the first round, the player with the highest seed (i.e., 1) would play with the player with the lowest seed (i.e., 64) which is designated Match No.1.

Similarly, the player with the second highest seed (i.e., 2) would play with the player with the second lowest seed (i.e., 63), which is designated Match No.2 and so on. In the second round, the winner of the Match No.1 of the first round would play with the winner of the Match No.32 of the first round and this match is designated Match No.1 of the second round.

If one of the matches was between the players seeded 23 and 46, then one of the matches in the tournament can be between players seeded

(a)9 and 13
(b)6 and 18
(c)5 and 51
(d)17 and 15
(e)None of these.

Answer: (a) 9 and 13

Nine persons namely P, Q, R, S, T, U, V, W and X were sitting in a linear row facing towards the South direction and were wearing different jersey numbers viz. 13, 18, 22, 25, 27, 32, 34, 36 and 40 not necessarily in the same order. The distance between each person is a consecutive multiple of '4m' from the left end. Note: The distance between any adjacent pair is not more than 35 m. The person wearing the Jersey numbered as 13 was at a distance of 40 m from the person wearing Jersey number 18. V was sitting to the left of the person who was wearing a Jersey numbered with a multiple of 17. The distance between S and X was 60 m and neither of them were sitting at any end. The distance between P and X is double the distance between S and U. Three persons were sitting between Q and the person wearing a jersey numbered in the multiple of 11. The person whose Jersey was numbered of a cube of a number was having one person between him and W. W was wearing an odd numbered Jersey. The person wearing the Jersey which was a Square of a number was sitting adjacent to P. More than three persons were sitting to the left of X. The Jersey number of S is less than that the Jersey number of R. R was not sitting at any end of the row. The person wearing the Jersey which was numbered as a square of a number was immediately right of the person whose Jersey was numbered half of it. The person wearing Jersey number 32 was sitting to the right of R. One who was wearing Jersey no. 22 was sitting adjacent to X.

Solve the problem and Tell me which person is wearing which jersey number. In Alphabetic order

Answer:
P = 22
Q = 36
R = 40
S = 34
T = 32
U = 27
V = 18
W = 13
X = 25

Twelve persons A, C, E, G, I, K, M, O, Q, S, U and W are working in the Indian Navy in different designations such as Admiral, Vice Admiral, Rear Admiral, Commodore, Captain, Commander, Lieutenant, Sub Lieutenant, Master Chief Petty Officer (MCPO), Chief Petty Officer (CPO), Petty Officer, Leading Seaman (LS) and Seaman.

Note: The designations are given in decreasing order, with Admiral being the senior most position and Seaman being the junior most position. There is no person designated at one post.

Constraints:

• K is junior to Vice admiral but senior to Lieutenant.
• W is two positions junior to K and senior to Sub Lieutenant.
• Only four persons are designated between M and W where M is neither Admiral nor Leading Seaman.
• One of the designations is vacant which is senior to Petty officer but junior to Captain.
• U is three positions junior to the vacant designation which is not Lieutenant.
• The number of persons junior to E is three less than the number of persons senior to U.
• E is neither Master Chief Petty Officer nor Commodore.
• Only six persons are designated between A and S who is four positions senior to the vacant designation.
• The number of designations between C and I is same as the number of designations between O and Q.
• Only one person is designated between Q and U.
• O is immediately junior to G.
• C is not junior to Sub Lieutenant.

Find who is in which post and give the answer as a table with two columns: Designation and Person (in decreasing order of designation).

Answer:
Admiral = G
Vice Admiral = O
Rear Admiral = C
Commodore = S
Captain = K
Commander = Vacant
Lieutenant = W
Sub Lieutenant = A
MCPO = U
CPO = I
Petty Officer = Q
Leading Seaman = M
Seaman = E