Junior : Final Hunt

FINAL HUNT

Without any trouble you are safely travelling towards your desination. It is just then that you come across a cave, in Nepal. The owl says that the cave is a short-cut, but the journey would be diff cult, with many obstacles along the way. Brilliant as you all are, you decide to take the challenge.

The cave is dark. One of you switches a ashlight on, and leads the way. Soon, you encounter a room with many book shelves. A door is on the other end of the room. As you observe the books, you notice that one book is very old, but the others are new. You realize that the old book may have the key for the door! You open the book and look through the pages. In the middle of the book, you see an odd fi gure, like the one below.

You think of a theory, and start solving the puzzle.

The lines originating from the centre, divide each pentagon into 10 equal parts or wedges.

The part between two immediate pentagons is a ring.

Remaining letters must be fi lled in such that:

1. Each ring must contain all the letters of the word “TOUCHLINES”

2. Every two adjacent wedges together must contain all letters of the word “TOUCHLINES”.

The above puzzle has four boxes. Starting from the outermost ring and going inwards, note the letters and compare with the options given below.

Question 19:

Which of the following is the correct answer?

(A)NEST 

(B) SHIN 

(C) ETCH 

(D) SLIT

You say the code word, and the door opens. You walk in, and look around the empty room. It is a dead end, but you see a poem on the wall. It reads:

As you dance each ____ around,

though once, once only,

Me, when you shall have found,

Do not hide your glee!

One of you notices that the code word fits in the blank of the poem. As you think about the poem, you see an arrow which directs your eyes downward. To your amazement, you fi nd the whole floor filled with letters and symbols!

You realize that you need to use the poem to find a solution to the puzzle under them.

The floor looked like this:

Rearrange the clues from the puzzle above, using the poem, to find a question and then answer it to get out of the cave.

Question 20:

What is the answer which can take you out of the cave?

(A) 07

(B) 70 

(C) 18 

(D) 81

You are running out of time but have no idea about the route from Nepal to IIT Guwahati. The various cut-out parts of the map that can help you reach IIT Guwahati are hidden in the houses shown in the fi gure below. You will get the parts of the map only on delivering the right article(one per house) to all the houses.

(i) An ‘X’ coloured ARTICLE should be delivered to an ‘X’ coloured HOUSE only by using an ‘X’ coloured TRUCK.

(ii) A truck can also carry other coloured articles so that it can place them at any of the CHECKPOINTS from where other truck can later carry it to the destination.

(iii) Trucks can carry any number of articles at a time.

(iv) The main objective is to start all the trucks at the same time, with same speed and deliver the

articles without collision of trucks. Also, a truck picks up every article that comes on its way.

(v) Last and the most importantly, the PATHS of the trucks should not overlap at any point other than

junctions. At junctions, the paths can though cross each other (but both trucks should not reach that junction at same time which leads to collision). The trucks can move only forward.

Question 21:

Draw the fi nal path of all the trucks and give the number of turns taken by the blue truck.

(A) 8 

(B) 7 

(C) 6 

(D) None of the above

Question 22:

Give the total number of articles carried by the red truck on it’s way.

(A) 1 

(B) 2 

(C) 3 

(D) 4

Hauts : Final Hunt

FINAL HUNT

You are running out of time. You now reach the outskirts of Nepal but have no idea about the route to

Assam. You then ask a person nearby for help. He helps you but through a puzzle. He shows you 12 boxes of diff erent sizes, each having two cavities(right and left) in which smaller boxes can be kept. He then numbers each box and places one inside the other randomly without showing you.The final result is a single box. He says, he will give you the correct map only if you tell which box is in

the right cavity of box numbered ‘2’. If you fi nd out the number of that box you will get the map.

Here are your clues:

1. If he unpacks all the boxes and arrange them in a line in the following way,

then the final numbering of boxes in which the boxes are arranged would be

5    11    4    2    7    6    1    8    10    3    12    9

2. If he unpacks all the boxes and arrange them in a line in the following way,

then the fi nal numbering of boxes in which the boxes are arranged would be

1    2    4    5    11    6    7    3    8    10    9    12

Question 21:

Which box is in the right cavity of ‘2’?

(A) 11 

(B) 6 

(C) 7 

(D) 5

Question 22:

If you found out the right box then also tell how many boxes of smallest size did he show you initially?

(A) 2 

(B) 3 

(C) 4 

(D) 5

The unfolding of the map came as a complete surprise. It was not the whole map but just a part of it. The instructions below will tell you how to get the other parts.

The rest of the parts are hidden in the houses shown in the figure below. You will get the parts of the map only on delivering the right article(one per house) to all the houses.

(i) An ‘X’ coloured ARTICLE should be delivered to an ‘X’ coloured HOUSE only by using an ‘X’ coloured TRUCK.

(ii) A truck can also carry other coloured articles so that it can place them at any of the CHECKPOINTS from where other truck can later carry it to the destination.

(iii) Trucks can carry any number of articles at a time.

(iv) The main objective is to start all the trucks at the same time, with same speed and deliver the

articles without collision of trucks. Also, a truck picks up every article that comes on its way.

(v) Last and the most importantly, the PATHS of the trucks should not overlap at any point other than

junctions. At junctions, the paths can though cross each other (but both trucks should not reach that junction at same time which leads to collision). The trucks can move only forward.

Question 23:

Draw the fi nal path of all the trucks and give the number of turns taken by the blue truck.

(A) 8 

(B) 7 

(C) 6 

(D) None of the above

Question 24:

Give the total number of articles carried by the red truck on it’s way.

(A) 1 

(B) 2 

(C) 3 

(D) 4

Junior : Treasure of Kabul

TREASURE OF KABUL

You then head towards Kabul. After reaching there, you come to know that the King’s descendant found an ancient-Treasure Box. One of the men of the ancient court discovered that that to open the treasure-box one has to fold the square papers with special magnetic ink in a ‘Heart’ like shaped region(as shown below) such that the ultimate shape we get is the shape with magnetic ink on the paper, so that this paper can be inserted in the keyhole of the treasure-box and open it. Help the descendant and get 10% of the treasure as reward.

Question 18:

What is the minimum number of folds required to complete the task?

(A) 8

(B) 9

(C) 10

(D) 11

Hauts : Tiling

TILING

You then head towards Kabul. After reaching there, you come to know that the King’s descendant found an ancient-Treasure Box. One of the men of the ancient court discovered that the code that unravels the treasure, is hidden in the below puzzles. Help the descendant and get 10% of the treasure as reward.

PUZZLE 1:

You are given ten ‘L’ shaped tiles of size 1 through 10. Stack tiles so that each tile is fully supported and also the stack is as high as possible. For example, we can stack L's of side 1 through 5 so that the stack is 18 units high and stack L’s of side 1 through 6 so that stack is 26 units high as shown in figures below.

[Note: It is not necessary that all the L’s should be present from one to 10]

Question 19:

What is the maximum height of the stack formed on stacking tiles of side 1 through 10?

And now, the shape of the stack gives you the shape of the key that unlocks the box but you still don’t know the size (in terms of number) of the key, which is hidden in the next puzzle.

PUZZLE 2:

A large square can be formed by small integer sided squares so that each square either lies on the bottom layer or lies on top of one or more larger squares. Some examples are shown below:

Question 20:

What is the smallest odd square that can be formed using above method?

Junior : On the Banks of Hari

ON THE BANKS OF HARI

After a day fi lled with adventures in Tehran, you now reach the bank of Hari river. There you find a box that contains the key to the boat which can help you cross the river quickly. The box can be opened only if the correct password is entered. On the top part of the box there is a number carved.

“101111830140311”

The box you have got can be opened by deciphering the code number given on the top of the box which would provide you the password. The password consists only English alphabets (capital). Each alphabet is coded by a three digit number in which the ones-place is given by the number of curved lines in that alphabet and the tens- place is given by the number of straight lines in the alphabet. To find the hundredths-place digit first place all the alphabets with the same last two digits together in their alphabetical order and interchange the fi rst half with the second half. Now number them 1 onwards and thus the corresponding number will take the hundredths-place.

Example: Let these letters (of some unknown alphabet) be the ones having one curved line and one

straight line in ascending order then they will be coded as-

(Consider “B” to have 2 curves and 1 straight line whereas “U” to have only a curved line. Also consider these letter as shown here: 

Question 16:

What is the correct password?

(A)SQYWD (B)SPIWD (C)SQIMJ (D)UPYMJ

As soon as you cross the river, you find a Kabuliwala. You ask him for help to reach Kabul as soon as possible. He says that he will show you the way to Kabul if you help him with the answer of a question. First he explains you the game of CROSS- ZERO.

“This game is played on a matrix of 3x3. In this game, the players try to get three circles or three crosses in a row (horizontal, vertical, or diagonal). A player always tries to win, i.e., if a player can place his own symbol (X or O) in a row that already contains two of his own symbols, he will do so. A player always tries to avoid that his opponent wins, i.e., if a player can place his own symbol (X or O) in a row that already contains two of the symbols of his opponent, he will do so.”

The question he asks is that Khaled and Shahzia play a game of Cross-Zero. Khaled plays with crosses (X) and Shahzia plays with circles (O); however we don’t know who started the game. The players are intelligent enough and maintain the rules. After six turns into the game the matrix looks like-

Question 17:

So who will win the game?

(a)Any one can win depending on the initial move

(b)Khaled

(c)Shahzia

(d)The game will result in a draw.

Hauts : Kabuliwala's Treasure

KABULIWALA'S TREASURE

After a day fi lled with adventures in Tehran, you now reach Kandahar. You realize that you are falling short of time and should reach Kabul as early as possible but the problem is that you have lost your map and you can’t see anybody nearby. So, you don’t know where to head towards. You suddenly see a Kabuliwala, whom you ask for help. 

He says, he will show you the way to Kabul only if you help him get his treasure. Then he takes you to a place which looks similar to a grid, which has some rocks, a xed metal ball gun and

a treasure box at the other end which can be opened only when the metal ball hits the 3 buttons. Now

help the Kabuliwala arrange those blocks in order to open the treasure box.

INSTRUCTIONS:-

1. The initial direction of ball cannot be changed. The metal ball once released only travels in straight lines unless and until it hits a rock.

2. Rocks re ect the ball when it hits them.

The place where you go looks something like the above figure. For the arrangement shown in the figure, the metal ball could only hit one button. Make appropriate shifts in the positions of rocks so that the ball can hit all the three buttons.

Question 17:

What is the sum of all the positions that have rock (including fi xed) on them?

(Two digit integer type)

After the kabuliwala leaves, you find another similar grid. Solve this one to have a treasure for yourself :-

WORMHOLE ROCK :- Acts as a teleport for the ball. How it exactly works is shown in the below 2 figures.

Question 18:

What is the sum of all the positions that have rock (including wormholes) on them?

(Two digit integer type)

Hauts and Junior : Coalesce

COALESCE

As you travel from Iraq towards IIT Guwahati, after a long time you find yourselves on a mountain trail at Tehran, Iran. The mountain trail is diff cult and slippery. You suddenly get caught in a landslide and fall into a deep hole. Then the stones of 2 kg weight start falling onto you from above.

The hole is a 4x4 grid i.e., it is divided into 16 squares. Each square can accommodate only one stone (of any weight). To survive, you need at least one empty square. Owl notices your trouble and gives you the magical power to meld together stones, but only those of the same mass can be mould together. Since the stones are falling very fast, you are only able to push the stones in straight lines (horizontally/vertically).

For example, when the arrangement of one of the rows in fi gure 1 when pushed horizontally to left transforms as shown:

Question 15:

If one stone falls every second, what is the maximum time for which you can survive i.e., when no square is empty and all stones become immovable?

(A) (2^16) -1

(B) (2^17) -1

(C) (2^17) - 2

(D) 2^16

Question 16:

What is the largest stone that you can make if every second, either 2kg stone or 4 kg stones fall?

(A) 2^17

(B) 2^16

(C) (2^16) -1

(D) (2^17)-2