### Below is the Question papers of Technothlon – 2016 and Click here for previous question papers of 2010-2015

Mario faces a door with a huge lock in front of him, requiring him to fill various alphabets in the different-looking lock as shown below.Just above the lock was written – ‘EACH CIRCLE IS UNIQUE’

Question 2 :

From the word MONSTER, how many letters are there in horizontal line containing ‘Z’ ?
(a) 1 (b) 2 (c) 3 (d) 4

After unlocking the door and entering, Mario met Mr. Quacky Turtle, the wise watchman of the castle and started moving towards him.

Question 3 :

Quacky found a paper in which product of two non-zero digits(1 to 8) is given. Similarly,Mario got sum of the same two numbers and then they are having a conversation.

1. Quacky says “I don’t know the numbers”.Mario says “I don’t know the numbers”.
2. Quacky says “I don’t know the numbers”.Mario says “I don’t know the numbers”.
3. Quacky says “I don’t know the numbers”.Mario says “I know the numbers”.

What is the product of the numbers ?
(a) 6 (b) 8 (c) 12 (d) 16

Question 4 :

Impressed by Mario’s answer, Quacky drags him into a chamber for a challenge.Chamber has two cells, A and B, with m dogs in one cell and n dogs in another. He also has a magical Dog Killer, which allows him to kill any number of dogs from any one of the cells or kill equal number of dogs from both the cells. For example, he can kill 4 dogs from A or 7 dogs from B or 3 dogs from both A and B. For winning the challenge, Mario must be the one killing the last dog. However, he realises that Quacky also has the same magical Dog Killer, and would take turns with him in order to try and get him killed.Quacky asks Mario to do the first move.How many dogs should Mario kill in his first move if cell A houses 12 dogs and B 15 dogs so that he can survive?
(a) 10 (b) 14 (c) 16 (d) 12

Question 5 :

To escape Quacky Turtle, Mario used a tunnel which was full of dirty water. To go out, he realized he had to drain all the water away, and immediately, he noticed that the valve box was locked by the lock shown below.15 plates numbered 1 to 15 were kept in the nearby rack, with the instruction, “The distance from plate numbered 1 to plate numbered 2 will be less than the distance from plate numbered 2 to plate numbered 3, which is less than the distance from 3 to 4, and so on”. Placing the plates on the unshaded circles, satisfying the conditions on board, find out the value of a+b (where a and b are the numbers to be filled in the indicated circles)

Note : Here Distance is calculated from centre of One Circle to centre to another Circle
(a)10 (b)12 (c)14 (d)16

Somehow Mario gets out of the tunnel and then finds himself face-to-face with the evil gorilla Donkey Kong.Looking down, he saw that he was standing on a gigantic chessboard.He could see various chessmen standing along the board. Donkey Kong shouted,“Domination, total domination! Three challenges, and I want domination in them all!”

Hint : In chess, domination problems mean arranging a minimum number of a specific type of chess piece such that all places on the board are attacked by atleast one peice.Total Domination: This is the same as domination but the spaces occupied by the attacking pieces should also be attacked by some other piece.

Question 6 :

What are the minimum number of moves knights have to make on the given 8*6 chess board so that in their final position, they dominate the entire chessboard if the initial position is as given in the figure beside?

(a)8 (b)10 (c)12 (d)None of these

Question 7 :

How many ways can you arrange 4 queens such that they will dominate a 5*9 chess board?
(a)4 (b)2 (c)6 (d)None of these

Question 8 :

A 8×8 chess board is in the shape of a torus, where the chess board is on the outer surface of the torus(as shown below). How many minimum number of Knights are required to totally dominate it?

(a)8 (b)10 (c)12 (d)None of these

Question 9 :

After beating Donkey Kong, Mario was informed by his friend Toad the Mushroom Guy that Bowser, the evil dragon who has kidnapped Princess Peach, uses a different language to communicate which is based on the English alphabets in matrices, and that the princess was not in the castle he was in! So, he decided to use the warp tunnel and left for the same. On reaching the warp zone, he saw the below pattern on the tunnel and realized that Bowser had put it there to prevent him from entering the warp zone. Figure the one important word which the sentence implied by this pattern on the Warp tunnel says to help Mario get out of the castle through the warp.Noticing his dilemma, Toad hinted that it is very well versed with the word. eodC dorW +*-!

Write down the 2nd letter of the word.

(a)S (b)H (c)I (d)V

Question 10 :

After somehow escaping from the previous castle, pangs of hunger grip him. Mario visits a chocolate store nearby where the shopkeeper has 9 jars filled with 4,2,6,7,3,4,5,8,3 jellyfishes respectively. Each second he is allowed to either double the content of one jar,or eat 9 jellyfishes (one from each jar).Can Mario always empty all the jars using these moves?If yes, then give the minimum time required to empty the jars ?

Question 11 :

He then enters a mushroom market. In the market, whenever two people greet each other,they have to swap their mushrooms. There are 64 people present in the Market.In order to save time, each pair of people is only allowed to greet each other atmost once. After a lot of greetings, Mario notices that it is no longer possible to return all mushrooms to their respective owners through more greetings. To sensibly resolve this maddening confusion,
he decides to bring in even more people (with more mushrooms), to allow for even more greetings and mushroom swappings. How many extra people are needed to return all mushrooms (including the extra ones) to their rightful owners?

Assume a person has exactly one mushroom.

Question 12 :

Further ahead in the market, Mario finds a huge bag containing 171 mushrooms. He reads the label – “Weighing from 1 to 171 kgs, all varieties within”. Mario is puzzled as he does not know which mushrooms weighs what. He goes to a stone seller who had an offer of “Buy 1, Get 2 Identical Stones Free”. Mario asks him for the different kinds of
stones and tells that he can use these to measure any of the mushroom accurately(using common balance). How many different kinds of stones does he buy?

(Minimum )

Question 13 :

As he reaches the exit of the market, Mario notices five people who are gathered for an eat-as-much-as-you-can competition. There is a clear order in their hunger (i.e. no two people are identically hungry) and the person who was more hungry initially (at the beginning of the competition) wins in a face-off. How many face-offs are required to rank everyone according to their initial hunger?

Note : Face-offs should be sufficient to guarentee rank of everyone in any case

After the market, Mario reaches the sea coast. Seeing this is the end of the road, he dives into the sea, unknown to the challenges that wait in his path.

Question 14 :

As he swam deeper, Mario bumped into Old Man Octopops, who, like his friend, Mr.Quacky Duck, is very fond of puzzles and weird games.

(i) Firstly, Octopops gives Mario to control three ‘squid’ pieces, while he himself controls a single ‘shark’ piece. Initially, all four pieces are placed somewhere along a straight line. They take turns making moves, with Mario going first. Each move, a player is allowed to move one of his pieces a distance of at most one unit along the straight line.Octopops wins if his ‘shark’ piece can catch one of the ‘squid’ pieces.
(ii) The same game is now played on a two-dimensional plane instead of a straight line.The rules are the same, except now Mario is given 20 ‘squid’ pieces.Can Octopops always win? Answer for both the questions.

(a) yes,no (b) yes,yes (c) no,no (d) no,yes

Question 15 :

Swimming further, he could feel something sucking the water out of the sea. He saw a huge 6ft × 6ft hole dug, which was pulling all the water. He has to fill it with some 2 × 2 square tiles and some 4 × 1 rectangular tiles. After arranging the tiles to cover the lava perfectly without overlap, excess pressure caused one of the tiles to smash. Unfortunately, the only spare tile is of the other shape to the one smashed. Will Mario be able to rearrange the remaining unsmashed tiles to perfectly cover the hole again?

(a) Yes (b) No (c) Yes,Only if broken tile is 4 × 1 (d) Yes,Only if broken tile is 2 × 2

Swimming deeper, a huge sewer comes in the line of sight of Mario. He dives inside it and the sewer closes. Swimming lower and lower, Mario finds himself inside Bowser’s Castle,where he can finally rescue Princess Peach. Out of the water, he finds himself staring at a huge door, with the heading ‘Bowser Inside’!

Question 16 :

Mario moves on to find a way to get through the main gates of Bowser’s chamber. He suddenly finds falling through a trapdoor and lands on something hard. The Devil Ghost Banshee , comes out and says, “This room is a standard 8×8 chessboard. Each of its 64 square is assigned a weight. These weights are assigned in such a manner that weight of
a square is an average of the weight of the square that it is surrounded by.” Mario now has to determine the weights of all 64 squares and for that Banshee tells him the weights of X squares. What could be the minimum value of X with which Mario can deduce the weights of every other square?

a) 8 b) 32 c) 56 d) None of these

Question 17 :

After crossing the chessboard path successfully, Mario now enters a dungeon where the next clue to get into the main chambers is hidden. In the dungeon, there is a row of 10 rooms and the Devil Ghost Banshee is in one of them. Each day, the ghost moves to an adjacent room. Mario now has to find the creature as soon as possible. But the problem is, Mario can open only one door in a day. What is the minimum no. of days that can guarentee Mario catch the ghost ?

(a) 10 (b) 13 (c) 16 (d) None of these

Question 18 :

After Mario catches the ghost, he questions Banshee of how to enter Bowser’s chamber.He stutters and tells him about the password that is hidden in the sacred clock chamber.Inside the clock chamber, he saw 7 weird clocks hanging from the ceiling, and the Banshee said,

He saw stairs going upwards with a keyboard below them, for typing the password to the castle. What is the password?

(a)ASTERIX (b)LUCIFER (c)THUMPER (d)RAPHAEL

Now Mario is at the centre of a circular room, where there are 49 doors around him.Also, he finds a staff, flicking it at a door will toggle 5 consecutive doors, beginning from the door it was flicked at, open doors will be closed while the closed doors will be opened.

Question 19 :

Mario’s aim is to apply this flickable staff several times to toggle the state of a single door. What are the possible number of times Mario would have to use this staff to achieve his aim?
(a) 25 (b) 32 (c) 40 (d) 49

Question 20 :

Now suppose, the staff toggles 15 consecutive doors then with how many doors can you acheive his aim of toggling a state of a single door ?
(a) 53 (b) 54 (c) 55 (d) None of these

Mario finally comes face to face with the evil dragon Bowser, who is ready to kill him,but, like all villains, he likes to play games before killing.So he throws up his favorite L-tromino challenge.

(Hint : An L-tromino is a 2 × 2 tile with one unit square removed)

Question 21 :

He changes the floor into a plate as shown below

And says his L-Tromino has 3 ground squares and 1 hole.
He says that he has used 8 L-Trominos on the floor and just 1 1×1 single warp tile, which can take him to the next level. However, the problem is that the warp tile looks like the ground tiles, exactly alike.

How many positions could the warp tile possibly be?

(a)1 (b)5 (c)9 (d)25

Question 22 :

For the final challenge, Bowser asks, “For which integers n, does there exist a shape which can be tiled using 2 × 1 dominoes in exactly n different ways?”

(a) All Natural Numbers
(b) n is power of 2
(c) n is an even number
(d) n = 2,4

2016 JUNIORS KEY

ENTRANCE TO THE CASTLE.

1. C
2. D
CASTLE LEVEL 1: WATCHMAN’S PATIENCE

3. C
4. C

THE SMELLY TUNNEL
5. D
CASTLE LEVEL 2 : DONKEY KONG’S CHALLENGE
6. B
7. D
8. A
INTERCEPTING THE CODE
9. C
OUT IN THE AIR!
10. 19
11. 02
12. 03
13. 07
UNDERWATER?
14. A
15. B
BOWSER’S CASTLE FOUND!
16. D
17. C
THE CLOCK CHAMBER
18. B
BOWSER’S CHAMBER – LEVEL 1
19. D
20. A
BOWSER’S CHAMBER – LEVEL 2
21. C
22. A