### Technothlon Previous Question Papers- Hauts Squad 2014

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2014 HAUTS SQUAD

###### Snap Deal

Now-a-days people are purchasing many goods through online shopping. By purchasing goods through online shopping, they can get their goods at reasonable prices. Snapdeal is one of the biggest and popular online shopping portals. According to Anuj, the manager, “Snapdeal offers “snapdeal coupons” using which prices can be further reduced. We follow a unique strategy to give coupons to customers”. When Aishwarya, a customer, purchased a product, the following table was displayed.

They asked him to construct a sequence in this format. The terms are based on only diagonal elements. For a particular diagonal element, the term in the sequence is formed by adding all previous diagonal alphabet numbers to that diagonal alphabet number. The coupon code is known by the price of the product. Eg: If sequence is ABCD……. and the product price is 143. The coupon is ADC

**Question 1**

The seventh term in the sequence is

A) I B) J C) P D) Q

**Question 2:**

If Aishwarya wants to purchase a laptop of price 46645, then coupon code is

A) IHSIR B) UNNIM C) LETNI

Midhul and seven of his friends go to Accoland, a famous amusement park in Guwahati.Against all odds they decide to play bumper cars. The available cars are of various colours blue, green, purple & red, and luckily there are exactly two of each colour. Hence, they decide to form teams of two, with each team occupying the cars of one particular colour.Midhul & Saichran are team-mates and so are Mayank & Kenil. The game proceeds and each member tries to bump as many opponent team members as possible. Team-mates obviously do not bump each other(not even by accident).If player A bumps player B, then player B will immediately take revenge and bump player A.The game comes to an end, and everyone enjoys themselves thoroughly. Midhul bumped Mayank just before the game ended. He is curious to know the status of the other players. He goes around and asks everyone (other than himself) how many distinct players they have bumped. Surprisingly, each of them gives a different answer (they have very good memory, and are completely honest) Answer the following questions:

**Question 3**

How many distinct players did Saicharan bump?

A) 1 B) 2 C) 3 D) 4

**Question 4**

How many distinct players did Midhul bump?

A) 1 B) 2 C) 3 D) 4

**Question 5**

Saicharan bumped:

A) Both Mayank & Kenil

B) Mayank but not Kenil

C) Kenil but not Mayank

D) Neither Kenil nor Mayank

Abhishek, father of Rishi gives him a big box of chocolates. However, before handing over the box to Rishi, Abhishek asks him to solve the Sliding Coins puzzle.Sliding coins is a puzzle in which an arrangement of coins is rearranged to another arrangement by sliding one coin at a time. There are following rules are according to which the rearrangement has to be done.

→ All coins are of the same size and shape, i.e., circular

→ All coins lie in a plane and cannot be kept one over the other.

→ A move involves sliding a coin to a new position that touches at least two other coins without disturbing any other coin during its motion.

Here is the puzzle which Rishi has to solve. Can you help him rearrange the arrangement at the left to that at the right given in the questions that follow?

**Question 6**

How many minimum number of moves are required to complete the task?

A) 9 B) 11 C) 14 D) None of these

**Question 7**

How many minimum number of moves are required to complete the task?

A) 6 B) 7 C) 8 D) None of these

**Question 8**

In the game show, ‘Who wants to be a millionaire’, Aarrushi has reached into the last stage of the game where she is required to answer a question that will make her win 1 million pounds. Akhil, the host of the show asks the following question to her, “I can give you money in orders of 6, 9 and 20 pounds. What is the largest amount of money I cannot give you?” What should be Aarrushi’s answer so as to be declared the winner of the show?

(How to answer? Answer the largest amount of money. Eg: if the answer is 12,then mark your answer as 0012)

**Question 9**

Jayadeep, a great archaeologist is trying hard to reconstruct the map of an ancient old kingdom. The kingdom was very large and consisted of many cities (between 180 and 200), which were connected to each other through one-way roads. After doing a lot of research, he finds some interesting clues. Each road had a fixed source city (start point)and a fixed destination city (end point), and the traffic is allowed to move only in the direction

from the source to the destination. Further, no two roads can have the same source and destination (i.e they are not identical). The kingdom is well connected such that between any two cities, there exists either a path with two roads or a path with a single road but not both. Also, for all cities there is always a route with exactly two roads, which starts at the given city and ends at the same (a loop). How many cities are there in the

kingdom?(How to answer? Answer the number of cities. Eg: if the answer is 100,then mark your

answer as 0100)

**Question 10**

One day Sumeha challenged Abhilasha to solve a new type of code that she had developed.She gave her a few clues about how the code works by giving her a few examples:

1. abc → acb → aaa → aaa → aaa

2. bcd → cbd → ddd → ddd → ddd

3. abcd → acac → acac → acac → acac

4. habit → baiai → aabai → aaaaa → aaaaa

In the above examples, the words have been transformed according to the logic of the code four times. When the word “TECHNICHE” undergoes the same logical transformation thrice, what is the word that Abhilasha obtains?

A) Eineeneih B) Eeeiheiee C) Heieeeeei D) Ieeeeeihe

**Question 11**

Consider a Rubik’s (3x3x3) cube with its faces having the colors green, blue, orange, yellow, red and pink such that

→ Blue is adjacent to green but not to yellow

→ Green is adjacent to red but not to orange

→It is known that some of the small cubes of the Rubik’s cube are defective. Here are some clues to identify them.

A number is mentioned on some of the cubes. This number implies the number of defective cubes among the cubes touching the cube on which the number is written. (For example:number of cubes touching center cube of the entire Rubik’s cube is 26)So here are the faces of Rubik’s cube with numbers on some of the cubes.

What are the number of defective pieces?

A) 8 B) 12 C) 16 D) 9

**Question 12**

There are 5 persons who are trapped in 5 different elevators. There are 49 floors in the building. The 5 persons are respectively on 17th, 26th, 20th, 19th, 31st floors. The elevator doors open only when all the elevators are between 21st and 25th floor in descending order. There are 2 buttons +8 and -13 that will be activated only when 2 elevators are selected together. The person on the 19th floor decides to take charge and get all of them out. What is the minimum number of moves in which he can accomplish the target?

A)10 B) 12 C) 14 D) 16

**Question 13**

Raghav has a great interest in Mathematics and is currently pursuing his B.tech in Mathematics and Computing at IIT Guwahati. He also does a part time job at Barbeque Nations. One day, Sumeet along with six of his best friends, Shreyas, Minkush, Shubham, Adesh,Umang and Snehit went to the restaurant for his birthday treat. They sit in the same order as their names have been listed above. Sumeet ordered a 420mL bottle of cranberry juice which has to be shared by all the 7 friends. Raghav in order to amaze them with his mathematical skills, went to each one of them and divided the juice in the 7 glasses unequally. He then asked Sumeet to divide his share into 6 equal parts and pour it into the glasses of rest of the 6 friends. In exactly the similar way, Raghav told Shreyas to divide his present share into 6 equal parts and pour it into the glasses of rest of the 6 friends. This went up in the same order as they are sitting, till all of them had done the same task. After all this sharing, the 7 friends still had the same amount that they had right in the beginning. Can you tell how much juice was served to Minkush?(How to answer? Answer the amount of juice(in mL).Eg: if the answer is 80,then mark youranswer as 0080)

Desh had recently read the novel ‘Angels and Demons’ and he was vastly impressed by the ancient brotherhood of Illuminati, a secret cult who believe “Science is the new God.” Being an enthusiast of Science, he researched about the organization in a hope to join it and was able to track their roots in modern-day Germany. He mailed to the Master Sabazius and Sabazius replied with a set of tasks for Desh’s initiation into the brotherhood.

**TASK 1**

The Illuminati consider the numbers 11, 13 and 33 as sacred. Sabazius has presented Desh with 11 cards (numbered 1 to 11) each having a unique positive integer, and the sum of numbers on all the cards equals 3313. The first 10 cards have numbers forming an increasing sequence, and the 11th card has a number which is greater than the number on the 10th card by n.To guess the sequence, Sabazius wrote: The world is about duality. To become an Illuminatus,

you must be twice the man you are now.To find n, Desh is posed with the following statement: n is the largest 3-digit number that is a fifth power.Desh must choose 3 cards among the 11, in such a way that the numbers on the cards chosen add up to 1333. There is only one way this can be done.

**Question 14**

What is the sum of the card numbers required to get the sum as 1333? (E.g. if cards 2,4,5 are required, answer should be 11.)

A) 24 B) 18 C) 16 D) 10

**TASK 2**

The Illuminati cult has a total of n (same as the earlier n) members presently. The members are divided into 3 classes: Novice, Minerval, and the Illuminated. Each class consists of a different number of members.Novice consists of groups of 11 each.Minerval consists of groups of 13 each.Illuminated consists of groups of 33 each. Desh is further told that Novice has the maximum number of groups and Illuminated has the minimum. Moreover, each class has a composite number of members.

**Question 15**

Which class must Desh join such that even after his initiation, the number of members in all the classes remains composite?

A) Novice B) Minerval C) Illuminated D) None of these

**TASK 3**

Supervising all the ‘n’ members is a group of 4 Masters called the Elite. The 4 are Sabazius,Baldur, Gerold and Dagmar. Sabazius is willing to initiate Desh directly into the Elite group, provided he can solve the third riddle.For a ritual of the Elites, the 4 Masters have come together and are staying at the LeonardoRoyale hotel. Desh has been invited to the hotel as the fifth Master.The hotel consists of 5 rooms and a small restaurant that contains 5 tables. Each Master has a rank, which shows his level of thinking with respect to the whole group. The master with the first rank is said to be the Grand Master, and it is not Desh. Rooms, as well as tables, are successively numbered from 1 to 5 in a way that each Master lives in a room and sits at a table different in number from his rank. To avoid confrontation, Masters with successive ranks are allowed neither to live in rooms next to each other nor to eat at tables next to each other. To become an Elite, Desh just has to figure out his rank, room no. and table number. It is known that:

→ Sabazius does not eat at the fifth table.

→ Baldur is not the Grand Master.

→ Sabazius has exactly the middle rank between Dagmar and Desh.

→ Baldur is more intelligent than Sabazius.

→ Gerold eats at a table next to Baldur.

→ Dagmar does not eat on a table with the same number as his room number.

**Question 16**

What is Desh’s table number among the Masters?

A) 2 B) 3 C) 4 D) 5

The given maze represents a grid where each block represents either land or water. The numbers (Not the encircled numbers) in some of the blocks denote the number of land-water boundaries surrounding that block. The blocks of land form one continuous mass, i.e,an island. The entire grid is surrounded by water.The encircled numbers denote people who are either trapped on the island or drowned in the water depending on the block in which they are present.

HINT: For the blocks of land to form one single mass, the land-water boundary should form

a closed, continuous loop

**Question 17**

If a rescue helicopter flies over the island to save survivors, how many people can be saved? (Hint: Drowned people cannot be rescued.)

A) 5 B) 6 C) 7 D) 8

**Question 18**

If 3 of the survivors are named Dulton, Harsh and Aneesh, what might be the name of one of the remaining survivors?

[HINT: I am a man connected to the number allotted to me,start taking my name and you have found me]

A) Bhavin B) Keshav C) Nikhil D) Rishab

Now, write the saved person’s number in a sequence such that a survivor in Row 1 Col 1(if there are any) comes first, one in Row 1 Col 2 comes second and so on. Note that not every row contains a survivor. Further, one row may contain multiple survivors. Repeat the last 3 terms of the sequence infinitely. The sequence thus obtained is called a Hailstone Sequence.Hailstone sequences are called so because they go up and down just like a hailstone in a cloud before crashing to the earth – like the repeating tail of the sequence. These are easy to describe but are one of Maths’ unsolved problems.

**Question 19**

Ajay’s teacher has assigned him the task of finding the general rule of the above sequence. Using this, he needs to figure out the number of terms between the first term and the first occurrence of 1 (both exclusive) if the sequence starts from 13.Can you help Ajay with this task?

A) 4 B) 6 C) 8 D) 10

**Question 20**

Following paragraph describes a way to encode a message:- Consider 4 letters of alphabet (A,B,C,D). Place these letters along a wheel in anticlockwise direction such that each letter subtends an angle of 90 degrees (this wheel would have 4 spokes) at the centre. Now the positions to which the letters correspond to is like if we want to encode ‘BAD’, ‘B’ would correspond to position 1, ‘A’ to position 2 and ‘D’ to position3.Now, the wheel is rotated by “ angle subtended * position number” for each letter and the new letter at that position of wheel would give us the code for the letter previously present at that position.In the above example, since B comes at position 1 we would rotate the wheel by “90*1=90 degrees clockwise” to get our code as explained in the figure.

this would encode our ‘B’ to ‘C’. similarly ‘BAD’ would convert to ‘CCC’.(it might seem awkward that 3 letters get encoded to same letter. think carefully you will realise it’s very simple indeed)Now consider 26 alphabets and 10 numbers, alphabets in order from A to Z followed by numbers from 0 to 9 such that you have 36 characters in all. and now use the above to decode the following message.(obviously this time the angle subtended would be 360/36=10 degrees and our wheel would have 36 spokes.)

‘H JLR9 NUW’

How many Consonants are there in the message that you have decoded?

Seven Blindfolded prisoners are pushed onto a hanging platform, which is open at both the ends. Below, there is a large pool of volcanic lava which is hot enough to instantly kill upon contact. The metal surface of the platform is steaming hot, so the prisoners must constantly walk at a minimum speed of 0.5m/s, to ensure that their legs are not burnt. Two prisoners walking in opposite directions, upon collision will reverse direction but continue to walk at the same speed. It is obvious that eventually all of them will fall off the platform. The

platform is 11m long, and the initial positions of the prisoners are as shown in the figure,but their initial directions (i.e. left or right) may be different. Solve the following questions running through the prisoner’s mind.

**Question 21**

Clearly, the total time taken for all the prisoners to fall off the platform depends on the initial orientation of each of the prisoners. Prisoner A notices that if they orient themselves in a particular manner, the total time can be maximized. What is the maximum possible total time?

A) 11 (B) 13 (C) 17 (D) None of these

**Question 22**

Prisoner B (the one with the bald head) is of the greedy kind, and thinks only for himself.The time taken for prisoner B to fall off the platform depends not only on his initial orientation but also on the initial orientation of the rest of the prisoners. What is the maximum time for which Prisoner B can stay alive?

A) 11 (B) 13 (C) 17 (D) None of these

**Question 23**

Prisoner C on the other hand is an accomplished mathematician. He is not worried by any of these “worldly” issues. Rather, he would like to spend the last few minutes of his life solving an interesting math problem. His favourite number is 13, and he would like to find out how many distinct initial orientations of prisoners would lead to a total of 13 collisions before all of them fall off. What is the answer to this problem?

A) 0 (B) 2 (C) 3 (D) 1

n an attempt to find more information about the first British voyage to India, two archaeologists Niraj and Venkat went on a excavation journey. On reaching a rather denser part of the forest, both of them fell down in a very deep moss covered cave, following through the cave they reached a door in front of which was kept a pillar with some inscribes. Going through it vigorously and carefully they were able to deduce that it was a kind of coded puzzle pillar. After more investigation around the pillar, delicate sampling and detailed analysis they came down to this, that the pillar dated further back in time than the first reported voyage of the British in India. The complete understanding of the pillar might bring about quite a big change in Medieval Indian history. The decoding of this is also really important at this moment because this code and the door behind it is their only way out the cave, and they are running out of supplies. Help them solve the mysteriously coded pillar.Pillar is

**Properties**

→ This is a pillar which is square in shape from top view.

→ It has a property that each row can rotate about the vertical axis.

→ Each column (adjacent columns) connected with the edges are always together and can be interchanged with the other edge columns

Here 2 & 3 are always together. And 1 & 4 are always together and can be interchangeable with 2 and 3.

**Question 24**

The code represents a sentence. Find the number of words in above sentence.

(Note: Sentence or word will form like this:-

Here word is “ HELP DUDE ”.

A) 12 (B) 6 (C) 9 (D) None of these

**Question 25**

What are the minimum number of moves required to get the final sentence?

A) 8 (B) 6 (C) 10 (D) 4

**Question 26**

When you divide the preceding number alphabet with succeeding number alphabet (get the remainder) and then sum it. What corresponding alphabet you get for that number if A-Z has been numbered from 1-26 respectively.

A) K (B) E (C) F (D) N

**Answer Key – Hauts Squad**

SnapDeal

1. B

2. MARKS TO ALL

Bumping Cars

3. C

4. C

5. B

Sliding Coins

6. B

7. B

Puzzles

8. 0043

9. 0182

10. C

11. D

12. D

13. 0080

Illuminated

14. B

15. A

16. B

Island & Hailstone

17. B

18. A

19. C

The Disc_Disguise

20. 0003

I am Blind

21. D

22. D

23. A

Coded Pillar

24. D

25. D

26. D

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