Technothlon: 2015

Thursday 23 July 2015

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

(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

(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

(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

(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

(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

(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

(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

(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

(D) 11

Hauts : Tiling

TILING

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

(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

(D) (2^17)-2

Junior : Enigmathic

ENIGMATHIC

As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equally, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the

group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left).

Question 10:

In short, among how many people should the prize money be divided equally if every person is self-centred and every time he/she votes, tries to get maximum bene fit?

After your suggestion, the people of Iraq pay you a little as a reward for your help. Later, on your way to a hotel you find some people debating on an issue. Help them resolve it and earn some more money in return for your favour.

Question 11:

The issue is:

The government of Iraq wants to issue ‘d’ denominations of coins (in whole numbers of dinars(Iraqi currency)) so that by using no more than 3 coins, citizens can pay any amount from 1 dinar to 36 dinar. Find the value of ‘d’ and all the ‘d’ denominations and give the sum of all these ‘d’ denominations?

(Ex: if d=3 and 3 denominations are {4,5,3}, answer= 4+5+3= 12.)

Question 12:

After resolving the issue, you stop at the hotel to take rest for the night. Unfortunately, the hotel is owned by Poseidon. Poseidon is Athena's greatest enemy. Poseidon, on knowing that you are coming from Parthenon(Temple of Athena), decides to make life awful for all of you. There are 32 rooms in the hotel and there are 32 identical looking keys. He gives them all and says that the second heaviest key is the one which opens your room. He also says that there is a balance (it compares two keys at a time) which can be used only N times ,where N is the minimum number of comparisons required to fi nd the second heaviest key. What is the value of N?

Question 13:

Next, just to make your life even more diffi cult, he says that while you are checking out of the hotel, you should pay him any amount(in integer value of dinars) exactly that he asks (the maximum that he can ask is 302 dinars). So, you decide to divide 302 dinars into ‘N’ diff erent pouches such that you can pay him any amount from 1 to 302 dinars by giving certain number of pouches. What is the minimum value of ‘N’?

[Note: The above 4 questions are 2-digit integer type i.e., the answer can be any integer from 00 to 99].

Hauts : Enigmathic

ENIGMATHIC

As you reach Iraq, you come across a poster mentioning a contest which could help you earn more money for your trip. So you decide to participate and below are the questions of the contest.

Question 12:

If you want to build a pile of 100 coins (1 and 2 dinars) such that, number of coins between any two ‘2’ dinar coins is not equal to five, then what are the maximum number of 2 dinar coins that can be included in the pile?

Question 13:

Minimum length of ruler required with 4 marks such that every two marks are at a diff erent distance is 6 as shown in the diagram.

Similarly, what is the minimum length of ruler required with 6 marks such that every two marks are at a diff erent distance?

Question 14:

(Ex: if d=3 and 3 denominations are {4,5,3}, answer= 4+5+3= 12.)

Hauts and Junior : Fragments

FRAGMENTS

While travelling through the Syrian Desert, you are in desperate need of water. The owl, still bursting with energy(God knows how) comes fl ying back to you to tell you that she had located a water faucet nearby. Hearing this, you rush to it, to fi nd a real water cooler. But the problem is, it has seven pieces lying on the ground which have to be fi tted to form a rectangle in order to have the faucet working.

Question 10:

Which of the following statements are correct about the rectangle formed?

(A) The corner four pieces are 1,3,5,7

(B) The corner four pieces are 1,2,5,6

(D) Rectangle cannot be formed

Suddenly, the Desert God emerges out of the faucet. He says, “I am pleased with your hard-work, and will reward you with food if you pass my challenge.” He gives you in finite number pieces of fi ve di fferent types as shown below with numbers etched on them. He then tells you to use a maximum of 30 of these pieces to make a rectangle such that the sum of the numbers on all of the small squares is maximum. Also, each type should be used at least once.

Question 11:

What is maximum sum of all the numbers that is possible?

(A) 137x4

(B) 136x4

(D) Rectangle cannot be formed

Junior : Safe Paths

SAFE PATHS

Question 7:

On your way to IIT Guwahati, you and your friends have to cross Aleppo. There are some safe one-way paths such that you can move only in east or south direction. Below is the map of those safe paths. You start at ‘H’ and need to reach ‘O’. The arrows show the direction you must follow on the way.

Find the number of di fferent routes that you can take to cross the desert.

(A) 440

(B) 86400

(D) 42

Hauts : Pyramid Walls

PYRAMID WALLS

Another break comes in your journey when you encounter a long wall in Aleppo. The wall is made of bricks of di fferent sizes and if you put all the bricks in order of their sizes, you will get a staircase and be able to cross it. So, you have to sort the bricks such that the smallest is on the top and largest at the bottom. To re-order them, you can hold any number of bricks from the top of pile, lift them, invert the pile you are holding and place the inverted pile back on the rest of the bricks below. The move has been explained in the below diagram:

The above diagram indicates one move or step. By doing a certain number of appropriate moves, you can bring the entire pile of bricks to suit your need.

The wall stopping your way looks like the figure shown:

You have to make the staircase by sorting the wall according to the rules explained above. As you are in hurry to complete your journey, you must sort the bricks in minimum possible moves.

Question 7:

What is the minimum no. of moves required?

(A) 10

(B) 9

(D) 12

After crossing the wall, your journey hits another wall (see below), but this time sorted and built of hollow numbered blocks. On reaching the top of it, you see a signboard which says: “From the top block, move down one layer a time to either of the two touching blocks just below the one where you are. At the bottom, you will find a glider which fl ies for as much time as the sum of the numbers on the blocks through which you pass”. As you would want the glider to fl y for as much time as possible, you must choose the path which gives you the maximum sum.

Question 8:
Find the path and give the maximum time for which the glider can be own.
(A) 248
(B) 335
(C) 249
(D) 250

Question 9:
Can you fi nd how many paths pass through the block ‘55’ ?
(A) 48
(B) 12
(C) 24
(D) 10

Junior : Crack The Code

CRACK THE CODE

Question 6:

You now reach Turkey. Tired by your journey, you decide to go sightseeing in the town of Istanbul. Inside the Hagia Sophia, while you are walking, you fi nd a key-ring which has two keys on it, with a keychain as shown below.

En route outside the castle, you fi nd out that the escape is through a channel, which has two doors one behind another. Above the fi rst door, it is written

“Alphabet starts with ‘a’ ”

“Look down to up, and you’ll see something interesting that satis es me”.

So you plug one of the keys into the door. A sentence appears on it, along with a keyboard.

“Alohomora”.

You decode what the sentence means and type in “eszrzxzbe”.

The gate opened, sucking in the key plugged in and exposing another gate, with another sentence

written “Incendio”.

Suddenly the owl faints due to very less oxygen and you are left to decode the code.

What do you type in to open the gate?

(A)syimylsz

(B)sylmyisz

(C)s flmfi sz

(D)s flmfi sz

Hauts : Crack The Code

CRACK THE CODE

Question 6:

You and your friend along with the owl now reach Turkey. Tired by your journey, you decide to go a bit sightseeing in the town of Istanbul. Inside the Hagia Sophia, while you all are walking, you encounter a weird looking signboard, which reads

“Lay down the letters,

Left it begins,

Right it goes,

Starting a new line”.

A trapdoor opens below you and you fall onto a gigantic chessboard. Overhead, you see a clock, which is rotating in the anticlockwise direction. Seeing this, you get puzzled.

Realizing that the only exit is an elevator across the board, you rush to it. There you nd a ghost guarding it. When asked about the exit, the ghost replies

”The board is all you have, follow lines, stay away from the edges, and watch the clock as it goes. ”

You realize that lift is not the exit and ask the Ghost what is to be done. He then gives you two words

"Powder and "Magic" and tells you to enter these words in their secret language following the clues. You decoded “Powder” as “hfvkma” . If this is the right word then what is “Magic” in their secret language?

(A) erfpk

(B) rfpkd

(D) erfpd

Hauts and Junior: Trouble With Flowers

TROUBLE WITH FLOWERS

The tourist guide at Parthenon takes you to an abandoned tunnel. And here you fi nd an inscribed stone and a bowl of colored fl owers. Suddenly you hear a deep and ancient gong ringing as you start reading the Stone Of Instructions. The instructions read as follows:

Every person entering the Temple of Athena will be given a bowl with 15 red fl owers and 12 yellow fl owers.
Each time the Gong of Time rings, he/she must do one of two things:
1. Exchange: If he has at least 3 red flowers in his bowl, then he may exchange 3 red fl owers for 2 yellow fl owers.
2. Swap: He may replace each yellow flower in his bowl with a red fl ower and replace each red flower in his bowl with a yellow flower. That is, if he starts with i red flowers and j yellow fl owers, then after he performs this operation, he will have j red fl owers and i yellow flowers.

[You can leave the tunnel only when you make all the combinations (no. of red, no. of yellow) of fl owers that are possible].

Question 4:
After how many operations will you have 5 each of red and yellow flowers?
(A) 5
(B) 10
(C) 15
(D) None of the above

Question 5:
What is the number of combinations you need to make to leave the tunnel?
(A) 27
(B) 52
(C) 54
(D) None of the above

The next day, on your way back from Parthenon, you see an owl injured under a large, old tree. You decide to save the owl and x its wing, so you take it along with you. Later you get to know that owl needs to reach IIT Guwahati, India as soon as possible. Realizing how dangerous it could be for the owl to travel to India, you decide to help the owl reach its destination.

Wednesday 22 July 2015

Hauts: Chess With A Twist

Chess With A Twist

Question 1.

Consider a chessboard of dimensions 4xN. What is the value of N among the following such that, you can start with a knight(horse) at some square of the board, proceed by valid moves, visit each square exactly once and can return to the starting point as the 4N+1st square? [Note: If the knight is at a position as shown figure, a valid knight move would be any square marked ‘X’]

(A) 2

(B) 4

(D) no such N exists

Question 2.

Consider a chessboard of dimensions 4xN. What is the value of N among the following such that, you can start with a knight(horse) at some square of the board, proceed by valid moves, and can visit each square exactly once, with no requirement that we ever return to the starting square?

(A) 2

(B) 4

(D) no such N exists

Question 3.

Find out the minimum number of moves required to move from the situation in the left to that in the right if the valid moves for bishop, rook, knight, king and pawn are shown in the gures below respectively.

(A) 9

(B) 18

(D) 8

So, what are you waiting for!! Go ahead & comment your solutions.

Junior: Chess Quizzer

Chess Quizzer

Question 1.

The picture demonstrates a 3x3 box with 4 knights denoted by the letters. W stands for a white knight and B for a black one. As in a standard game of chess, the knight can move only two steps in the horizontal or vertical direction and then one step in the other direction for one move. The objective of the game is to interchange the position of both the black and white knights. What is the minimum number of moves required to complete the game?

(A) 8

(B) 12

(D) 18

Question 2.

You have one knight, one king, one queen, one rook and one pawn each of the same colour. Arrange all fi ve of these pieces on the chessboard shown such that the following conditions are satis ed:

(i) The no. of pieces attacking a square(with a number on it) should be equal to the number written on it.

(ii) There should not be any piece on a square which has a number written on it.

[Note: A king can only attack its adjacent squares, a pawn attacks its diagonally adjacent squares, a rook on its horizontal and vertical lines, a queen on its horizontal, vertical and diagonal lines and a knight as explained in question 1. Lastly, rook and queen cannot attack a square if there is a some other piece in the path of attack.]

What should be the position of the Queen?

(A) B1

(B) B2

(D) A2

Question 3.

What is the minimum number of moves required to move from the situation in the left to that in the right if the valid moves for bishop, rook, knight, king and pawn are shown below?

(A) 9

(B) 18

(D) 8

Go ahead, comment your solutions.